Predicting NFL Statistics
Rich Lindberg
March 27, 2017
Predicting NFL Stats
The goal of this capstone project was to set a baseline linear regression for predicting NFL statistics. The use of the analysis would be to project player performance and see if the team I am working with needs to consider making adjustments given various factors of the upcoming game/season.
Where to get the data
I went to the website http://armchairanalysis.com/data.php. I have a subscription to the database, so I connected into it via SQL. I downloaded the historical database onto my hard drive, and mapped it in MySQL.
I then queried the DB to get the fields I would need. This operation took extensive time, so once it ran, I exported to a csv file, then read the csv into R.
suppressMessages(library(dplyr))## Warning: package 'dplyr' was built under R version 3.3.2suppressMessages(library(tidyr))## Warning: package 'tidyr' was built under R version 3.3.2suppressMessages(library(ggplot2))## Warning: package 'ggplot2' was built under R version 3.3.2suppressMessages(library(reshape2))## Warning: package 'reshape2' was built under R version 3.3.2suppressMessages(library(caTools))## Warning: package 'caTools' was built under R version 3.3.3suppressMessages(library(caret))## Warning: package 'caret' was built under R version 3.3.3suppressMessages(library(GGally))## Warning: package 'GGally' was built under R version 3.3.3nfl_data <- read.csv("NFL_offense.csv")The data is pretty clean from armchairanalyis, fivethirtyeight.com uses this website for its sports data, so it is a pretty reputable site.
I felt there were pieces of data either missing, or needing cleaning up. This brought on the fun process of cleaning and tidying the data.
Weather and field conditions
From a qualitative perspective, we know that field turf and ideal temperatures are the least inhibitive towards speed, according to players themselves. I wanted to identify extremes and hinderences.
I replaced all “NULL” temp fields with a generic “room” temperature assumption.
cold_weather and hot_weather were fields created to identify extreme ends of the temperature spectrum, and see if they have an impact on play
#make all null temperatures at game time "room" temperature
nfl_data$temp[nfl_data$temp == "NULL"] <- 70
nfl_data$temp <- as.integer(nfl_data$temp)
#highlight temp extremes
nfl_data <- mutate(nfl_data, cold_weather= ifelse(temp < 45, 1,0))
nfl_data <- mutate(nfl_data, hot_weather= ifelse(temp > 85, 1,0))
#weather factors
nfl_data <- mutate(nfl_data, grass_1 = ifelse(surf == "DD GrassMaster" | surf == "Grass",
1,0))
nfl_data <- mutate(nfl_data, bad_weather_1 = ifelse(cond == "Light Rain" |
cond == "Rain" |
cond == "Flurries" |
cond == "Snow" |
cond == "Foggy" |
cond == "Windy" |
cond == "Hazy" |
cond == "Thunderstorms"|
cond == "Light Snow" |
cond == "Light Showers" ,1,0))Home field advantage
Do players play better at home?
#identify home team
nfl_data$h <- as.character(nfl_data$h)
nfl_data$team <- as.character(nfl_data$team)
nfl_data <- mutate(nfl_data, home_team_1= ifelse(h == team, 1,0))Positions
Ignoring player stats, does the position matter
#identify position
nfl_data <- mutate(nfl_data, is_WR = ifelse(pos1 == "WR", 1,0))
nfl_data <- mutate(nfl_data, is_TE = ifelse(pos1 == "TE", 1,0))
nfl_data <- mutate(nfl_data, is_RB = ifelse(pos1 == "RB", 1,0))
nfl_data <- mutate(nfl_data, is_QB = ifelse(pos1 == "QB", 1,0))Age
Every year players get older, so we want to know “Does father time impact player performance?”
#age
nfl_data <- mutate(nfl_data, age = year - yob)Combine cleanup
The NFL combine is an event where prospective new players work out for the entire league to see. Their physical measurements are taken, and people find merit in this event. I wanted to see if these stats had any impact on player performance. Not all players attend the combine. For the fields where there are zeroes for the combine stat, I took the average for all non-zero stats for that position. This basically implies if you didn’t attend the combine, your stats are middle of the road.
#replace 0 forty with avg for position
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(forty1 = ifelse(forty == 0, mean(forty[forty>0]), forty))
#replace 0 vertical with average for position
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(vertical1 = ifelse(vertical == 0, mean(vertical[vertical>0]), vertical))
#replace 0 arm length with formula for 40% of height is arm
nfl_data$arm <- ifelse(nfl_data$arm == 0, nfl_data$height*0.4, nfl_data$arm)
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(shuttle1 = ifelse(shuttle == 0, mean(shuttle[shuttle>0]), shuttle))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(cone1 = ifelse(cone == 0, mean(cone[cone>0]), cone))NFL Teams
I created fields for teams (1 if player plays for that team in the header 0 if it doesn’t). I also cleaned up one team: The St Louis/LA Rams. The Rams moved in 2016 to LA, so the conditions of stadium changed. I combined the field into a single field.
#clean teams and give each team a field
nfl_data <- mutate(nfl_data, Teams = ifelse(team == "STL" | team == "LA", "STL/LA",team))
nfl_data <- mutate(nfl_data, ARI = ifelse(Teams == "ARI",1,0))
nfl_data <- mutate(nfl_data, ATL = ifelse(Teams == "ATL",1,0))
nfl_data <- mutate(nfl_data, BAL = ifelse(Teams == "BAL",1,0))
nfl_data <- mutate(nfl_data, BUF = ifelse(Teams == "BUF",1,0))
nfl_data <- mutate(nfl_data, CAR = ifelse(Teams == "CAR",1,0))
nfl_data <- mutate(nfl_data, CHI = ifelse(Teams == "CHI",1,0))
nfl_data <- mutate(nfl_data, CIN = ifelse(Teams == "CIN",1,0))
nfl_data <- mutate(nfl_data, CLE = ifelse(Teams == "CLE",1,0))
nfl_data <- mutate(nfl_data, DAL = ifelse(Teams == "DAL",1,0))
nfl_data <- mutate(nfl_data, DEN = ifelse(Teams == "DEN",1,0))
nfl_data <- mutate(nfl_data, DET = ifelse(Teams == "DET",1,0))
nfl_data <- mutate(nfl_data, GB = ifelse(Teams == "GB",1,0))
nfl_data <- mutate(nfl_data, HOU = ifelse(Teams == "HOU",1,0))
nfl_data <- mutate(nfl_data, IND = ifelse(Teams == "IND",1,0))
nfl_data <- mutate(nfl_data, JAC = ifelse(Teams == "JAC",1,0))
nfl_data <- mutate(nfl_data, KC = ifelse(Teams == "KC",1,0))
nfl_data <- mutate(nfl_data, MIA = ifelse(Teams == "MIA",1,0))
nfl_data <- mutate(nfl_data, MINN = ifelse(Teams == "MIN",1,0))
nfl_data <- mutate(nfl_data, NE = ifelse(Teams == "NE",1,0))
nfl_data <- mutate(nfl_data, NOR = ifelse(Teams == "NO",1,0))
nfl_data <- mutate(nfl_data, NYG = ifelse(Teams == "NYG",1,0))
nfl_data <- mutate(nfl_data, NYJ = ifelse(Teams == "NYJ",1,0))
nfl_data <- mutate(nfl_data, OAK = ifelse(Teams == "OAK",1,0))
nfl_data <- mutate(nfl_data, PHI = ifelse(Teams == "PHI",1,0))
nfl_data <- mutate(nfl_data, PIT = ifelse(Teams == "PIT",1,0))
nfl_data <- mutate(nfl_data, SD = ifelse(Teams == "SD",1,0))
nfl_data <- mutate(nfl_data, SEA = ifelse(Teams == "SEA",1,0))
nfl_data <- mutate(nfl_data, SF = ifelse(Teams == "SF",1,0))
nfl_data <- mutate(nfl_data, STL = ifelse(Teams == "STL/LA",1,0))
nfl_data <- mutate(nfl_data, TB = ifelse(Teams == "TB",1,0))
nfl_data <- mutate(nfl_data, TEN = ifelse(Teams == "TEN",1,0))
nfl_data <- mutate(nfl_data, WAS = ifelse(Teams == "WAS",1,0))Receiving Stats
For receiving, I wanted to get every players average: * yards * receptions * targets * touchdowns
I also wanted to get every position average, and average for team. Rationale for at least having that info is this: Compare player to team to league wide position
#calculate the averages by player, position, and team
#receiving
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_recy_plyr = mean(recy))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_recy_pos = mean(recy))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_recy_team = mean(recy))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_rec_plyr = mean(rec))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_rec_pos = mean(rec))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_rec_team = mean(rec))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_trg_plyr = mean(trg))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_trg_pos = mean(trg))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_trg_team = mean(trg))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_rectd_plyr = mean(tdrec))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_rectd_pos = mean(tdrec))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_rectd_team = mean(tdrec))Running Stats
I followed a similar process from up above.
The stats I was looking for the mean for were: * rushing attempts * rushing yards * fumbles
#running
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_rbra_plyr = mean(ra))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_rbra_team = mean(ra))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_rbra_pos = mean(ra))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_rbry_plyr = mean(ry))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_rbry_team = mean(ry))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_rbry_pos = mean(ry))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_fuml_plyr = mean(fuml))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_fuml_team = mean(fuml))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_fuml_pos = mean(fuml))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_tdr_plyr = mean(tdr))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_tdr_pos = mean(tdr))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_tdr_team = mean(tdr))Passing
I followed a similar process from up above.
The stats I was looking for the mean for were: * passing yards * passing attempts * passing completions * passing touchdowns * interceptions
#passing
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_qbpy_plyr = mean(py))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_qbpy_team = mean(py))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_qbpy_pos = mean(py))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_qbpc_plyr = mean(pc))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_qbpc_team = mean(pc))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_qbpc_pos = mean(pc))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_qbints_plyr = mean(ints))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_qbints_team = mean(ints))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_qbints_pos = mean(ints))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_qbtdp_plyr = mean(tdp))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_qbtdp_team = mean(tdp))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_qbtdp_pos = mean(tdp))
nfl_data <- nfl_data %>%
group_by(player.1)%>%
mutate(avg_qbpa_plyr = mean(pa))
nfl_data <- nfl_data %>%
group_by(Teams)%>%
mutate(avg_qbpa_team = mean(pa))
nfl_data <- nfl_data %>%
group_by(pos1)%>%
mutate(avg_qbpa_pos = mean(pa))Pre-Analysis exploration
I wanted to learn a little about the data. I had approximately 100 fields to choose from, so it is hard to infer if there were any correlations or other patterns off hand. I built a subset of the fields I wanted to explore. I named this subset: nfl_data_fields
I then created a correlation matrix:
nfl_data_fields<- subset(nfl_data, select = c("height", "weight", "cold_weather", "hot_weather",
"home_team_1", "temp",
"forty1", "vertical1", "ARI", "ATL", "BAL", "BUF",
"CAR", "CHI", "CIN", "CLE", "DAL", "DEN", "DET", "GB", "HOU", "IND",
"JAC", "KC", "MIA", "MINN", "NE", "NOR", "NYG", "NYJ", "OAK", "PHI", "PIT",
"SD", "SEA", "STL", "TB", "TEN", "WAS",
"avg_recy_plyr","avg_recy_pos","avg_recy_team","avg_rec_plyr","avg_rec_pos",
"avg_rec_team", "avg_trg_plyr","avg_trg_pos","avg_trg_team","avg_rectd_plyr",
"avg_rectd_pos","avg_rectd_team","avg_tdr_plyr","avg_tdr_pos","avg_tdr_team",
"avg_rbra_plyr","avg_rbra_pos", "avg_rbra_team","avg_rbry_plyr","avg_rbry_pos",
"avg_rbry_team","avg_fuml_plyr","avg_fuml_pos", "avg_fuml_team","avg_qbpy_plyr",
"avg_qbpy_pos", "avg_qbpy_team","avg_qbpa_plyr","avg_qbpa_pos","avg_qbpa_team",
"avg_qbpc_plyr","avg_qbpc_pos", "avg_qbpc_team","avg_qbints_plyr", "avg_qbints_pos",
"avg_qbints_team","avg_qbtdp_plyr","avg_qbtdp_pos","avg_qbtdp_team","grass_1",
"bad_weather_1"))
cor_nfl <- cor(nfl_data_fields)If you were to run cor_nfl, the print out is extremely difficult to read and gets cut off because of it’s size.
I decided a simpler view should be created, so I created an image of the matrix
image(cor_nfl)
This gives a pretty interesting view of the data, but is still hard to interpret. That being said, it was on the right path.
I then used qplot to get a better view of the data. With qplot I can control the colors, and since correlation matrices range from -1 to 1, setting the bookends of the color spectrum based on the values of the correlation would give me a very indicative heatmap
qplot(x=Var1, y=Var2, data=melt(cor(nfl_data_fields)), fill=value, geom="tile")+
scale_fill_gradient2(limits=c(-1, 1))+
theme(axis.text.x = element_text(angle = 90, hjust = 1, size = 5),
axis.text.y = element_text(size = 5))
There are strong relationships where we calculated general averages for the position, teams and players. That is not surprising since a stat like rushing will have strong relationships with how many attempts you make at rushing the ball. Typically, if you are running the ball more, you should see more yards. Obvious, but this confirms the correlation.
We then have to remove the highly correlated data fields.
highlyCor_nfl_data_fields1 <- findCorrelation(cor_nfl, cutoff = .8)
highlyCor_nfl_data_fields1## [1] 44 47 62 41 50 70 64 67 77 65 71 68 74 73 46 40 43 42 66 45 72 51 69
## [24] 53 60 56 52 55 6highlyCor_nfl_data_fields2 <- findCorrelation(cor_nfl, cutoff = .85)
highlyCor_nfl_data_fields2## [1] 44 47 62 41 50 70 64 67 77 65 71 68 74 73 46 40 42 66 45 72 51 69 53
## [24] 60 56 52 55highlyCor_nfl_data_fields3 <- findCorrelation(cor_nfl, cutoff = .9)
highlyCor_nfl_data_fields3## [1] 44 47 62 41 70 64 67 77 65 71 68 74 76 46 40 42 66 45 72 51 69 53 56
## [24] 52 55filtered_nfl_data_fields <-nfl_data_fields
filtered_nfl_data_fields <- filtered_nfl_data_fields[,-highlyCor_nfl_data_fields1]
filtered_nfl_data_fields## # A tibble: 39,255 × 51
## height weight cold_weather hot_weather home_team_1 forty1 vertical1
## <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 73 217 0 0 0 4.400000 38.50000
## 2 70 209 0 0 0 4.550000 34.80631
## 3 73 190 0 0 0 4.580000 38.00000
## 4 74 225 0 0 0 4.794693 31.82285
## 5 72 189 0 0 1 4.410000 36.50000
## 6 72 209 0 0 1 4.830000 32.00000
## 7 71 200 0 0 1 4.410000 36.07315
## 8 75 248 0 0 1 4.670000 37.50000
## 9 73 190 0 0 0 4.463801 36.07315
## 10 72 180 0 0 0 4.463801 36.07315
## # ... with 39,245 more rows, and 44 more variables: ARI <dbl>, ATL <dbl>,
## # BAL <dbl>, BUF <dbl>, CAR <dbl>, CHI <dbl>, CIN <dbl>, CLE <dbl>,
## # DAL <dbl>, DEN <dbl>, DET <dbl>, GB <dbl>, HOU <dbl>, IND <dbl>,
## # JAC <dbl>, KC <dbl>, MIA <dbl>, MINN <dbl>, NE <dbl>, NOR <dbl>,
## # NYG <dbl>, NYJ <dbl>, OAK <dbl>, PHI <dbl>, PIT <dbl>, SD <dbl>,
## # SEA <dbl>, STL <dbl>, TB <dbl>, TEN <dbl>, WAS <dbl>,
## # avg_trg_team <dbl>, avg_rectd_plyr <dbl>, avg_tdr_team <dbl>,
## # avg_rbra_team <dbl>, avg_rbry_plyr <dbl>, avg_rbry_pos <dbl>,
## # avg_fuml_plyr <dbl>, avg_fuml_team <dbl>, avg_qbints_team <dbl>,
## # avg_qbtdp_plyr <dbl>, avg_qbtdp_team <dbl>, grass_1 <dbl>,
## # bad_weather_1 <dbl>qplot(x=Var1, y=Var2, data=melt(cor(filtered_nfl_data_fields)), fill=value, geom="tile")+
scale_fill_gradient2(limits=c(-1, 1))+
theme(axis.text.x = element_text(angle = 90, hjust = 1, size = 5),
axis.text.y = element_text(size = 5))
I tested cutoffs at 0.8, 0.85, 0.9 correlation, then removed the columns that were highly correlated at the 0.8 level.
Receiving Regressions
We have to set up our test and training data with preProcess:
set.seed(123)
split <- sample.split(nfl_data$recy, SplitRatio = 0.7)
TrainRecy <- subset(nfl_data, split == TRUE)
TestRecy <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(TrainRecy, method = c("center", "scale"))
trainTransformed <- predict(preProcValues, TrainRecy)
testTransformed <- predict(preProcValues, TestRecy)We then inspect the relationships of the columns using ggpairs
ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[46:51]))])
Now that we are ready to train and test the data, let’s do it!
Receiving Yards first run
#formula for not having to write everything out
wrrecyregform <- formula(paste("recy ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
#first run of the recy regression
linRegrecy <- lm(wrrecyregform, data = trainTransformed)
summary(linRegrecy)##
## Call:
## lm(formula = wrrecyregform, data = trainTransformed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5035 -0.4258 -0.1162 0.2367 7.5163
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.166e-15 4.840e-03 0.000 1.000000
## height 3.793e-03 9.391e-03 0.404 0.686273
## weight -6.979e-02 8.801e-03 -7.930 2.27e-15 ***
## cold_weather -1.778e-02 5.095e-03 -3.490 0.000483 ***
## hot_weather -6.230e-03 4.884e-03 -1.276 0.202139
## home_team_1 -4.595e-03 5.266e-03 -0.873 0.382930
## forty1 -4.717e-02 8.353e-03 -5.648 1.64e-08 ***
## vertical1 2.689e-03 6.422e-03 0.419 0.675408
## ARI 2.401e-02 6.770e-03 3.547 0.000390 ***
## ATL 2.804e-02 6.803e-03 4.121 3.78e-05 ***
## BAL 2.715e-02 6.809e-03 3.988 6.69e-05 ***
## BUF 9.928e-03 6.721e-03 1.477 0.139647
## CAR 2.115e-02 6.677e-03 3.168 0.001537 **
## CHI 2.497e-02 6.603e-03 3.782 0.000156 ***
## CIN 2.112e-02 6.724e-03 3.141 0.001683 **
## CLE 3.780e-02 6.693e-03 5.648 1.64e-08 ***
## DAL 1.258e-02 6.761e-03 1.860 0.062893 .
## DEN 1.054e-02 6.787e-03 1.553 0.120447
## DET 2.404e-02 6.694e-03 3.591 0.000330 ***
## GB -1.135e-03 6.891e-03 -0.165 0.869180
## HOU 2.902e-02 6.809e-03 4.262 2.03e-05 ***
## IND 1.928e-02 6.759e-03 2.853 0.004333 **
## JAC 1.586e-02 6.593e-03 2.406 0.016145 *
## KC 2.082e-02 6.738e-03 3.090 0.002005 **
## MIA 2.199e-02 6.629e-03 3.317 0.000910 ***
## MINN 2.172e-02 6.670e-03 3.257 0.001128 **
## NE 1.683e-02 6.966e-03 2.416 0.015712 *
## NOR 1.276e-02 6.945e-03 1.838 0.066058 .
## NYG 2.344e-02 6.788e-03 3.453 0.000555 ***
## NYJ 1.344e-02 6.763e-03 1.987 0.046912 *
## OAK 2.270e-02 6.805e-03 3.335 0.000853 ***
## PHI 2.565e-02 6.594e-03 3.889 0.000101 ***
## PIT 3.283e-02 6.768e-03 4.851 1.24e-06 ***
## SD 2.251e-02 6.641e-03 3.390 0.000701 ***
## SEA -9.863e-04 6.892e-03 -0.143 0.886212
## STL 2.074e-02 6.708e-03 3.091 0.001994 **
## TB 1.931e-02 6.645e-03 2.906 0.003662 **
## TEN 1.884e-02 6.686e-03 2.819 0.004826 **
## WAS 2.807e-02 6.721e-03 4.176 2.98e-05 ***
## avg_trg_team NA NA NA NA
## avg_rectd_plyr 5.388e-01 6.181e-03 87.171 < 2e-16 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr 4.959e-02 7.396e-03 6.704 2.06e-11 ***
## avg_rbry_pos -7.121e-02 8.618e-03 -8.263 < 2e-16 ***
## avg_fuml_plyr -6.954e-03 7.150e-03 -0.973 0.330717
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -4.310e-02 7.766e-03 -5.550 2.88e-08 ***
## avg_qbtdp_team NA NA NA NA
## grass_1 -1.362e-02 5.569e-03 -2.446 0.014435 *
## bad_weather_1 -9.516e-03 4.924e-03 -1.933 0.053285 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8024 on 27438 degrees of freedom
## Multiple R-squared: 0.3572, Adjusted R-squared: 0.3562
## F-statistic: 338.9 on 45 and 27438 DF, p-value: < 2.2e-16#updating formula to take out insignigicant values
linRegrecy2 <- update(linRegrecy, ~. -height- hot_weather - home_team_1-vertical1-BUF-DAL-DEN-GB
-NE-NOR-NYJ-SEA
-avg_trg_team-avg_tdr_team-avg_rbra_team-avg_fuml_plyr-avg_fuml_team
-avg_qbints_plyr
-avg_qbints_team-avg_qbtdp_team-bad_weather1)
summary(linRegrecy2)##
## Call:
## lm(formula = recy ~ weight + cold_weather + forty1 + ARI + ATL +
## BAL + CAR + CHI + CIN + CLE + DET + HOU + IND + JAC + KC +
## MIA + MINN + NYG + OAK + PHI + PIT + SD + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr +
## grass_1 + bad_weather_1, data = trainTransformed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5054 -0.4250 -0.1179 0.2419 7.5182
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.958e-15 4.841e-03 0.000 1.000000
## weight -6.782e-02 6.074e-03 -11.166 < 2e-16 ***
## cold_weather -1.826e-02 5.027e-03 -3.633 0.000281 ***
## forty1 -4.715e-02 7.051e-03 -6.688 2.31e-11 ***
## ARI 1.650e-02 5.038e-03 3.276 0.001055 **
## ATL 2.042e-02 5.046e-03 4.046 5.22e-05 ***
## BAL 1.901e-02 5.037e-03 3.774 0.000161 ***
## CAR 1.360e-02 5.061e-03 2.688 0.007196 **
## CHI 1.753e-02 5.039e-03 3.480 0.000503 ***
## CIN 1.302e-02 5.025e-03 2.592 0.009558 **
## CLE 3.025e-02 5.083e-03 5.952 2.68e-09 ***
## DET 1.641e-02 5.030e-03 3.262 0.001107 **
## HOU 2.169e-02 5.050e-03 4.295 1.76e-05 ***
## IND 1.164e-02 5.028e-03 2.315 0.020637 *
## JAC 8.591e-03 5.054e-03 1.700 0.089151 .
## KC 1.333e-02 5.089e-03 2.619 0.008814 **
## MIA 1.431e-02 5.038e-03 2.840 0.004509 **
## MINN 1.413e-02 5.034e-03 2.807 0.005003 **
## NYG 1.506e-02 5.029e-03 2.995 0.002748 **
## OAK 1.522e-02 5.107e-03 2.981 0.002877 **
## PHI 1.798e-02 5.034e-03 3.572 0.000355 ***
## PIT 2.492e-02 5.070e-03 4.915 8.93e-07 ***
## SD 1.471e-02 5.072e-03 2.900 0.003736 **
## STL 1.295e-02 5.044e-03 2.567 0.010260 *
## TB 1.131e-02 5.055e-03 2.238 0.025231 *
## TEN 1.124e-02 5.074e-03 2.216 0.026724 *
## WAS 2.014e-02 5.065e-03 3.977 7.01e-05 ***
## avg_rectd_plyr 5.400e-01 6.058e-03 89.139 < 2e-16 ***
## avg_rbry_plyr 4.662e-02 6.950e-03 6.708 2.01e-11 ***
## avg_rbry_pos -7.177e-02 7.494e-03 -9.577 < 2e-16 ***
## avg_qbtdp_plyr -4.698e-02 5.863e-03 -8.012 1.17e-15 ***
## grass_1 -1.750e-02 5.304e-03 -3.299 0.000971 ***
## bad_weather_1 -9.620e-03 4.917e-03 -1.957 0.050395 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8025 on 27451 degrees of freedom
## Multiple R-squared: 0.3567, Adjusted R-squared: 0.356
## F-statistic: 475.8 on 32 and 27451 DF, p-value: < 2.2e-16#updating formulas to remove any insignificant values
linRegrecy3 <- update(linRegrecy2, ~. -JAC)
summary(linRegrecy3)##
## Call:
## lm(formula = recy ~ weight + cold_weather + forty1 + ARI + ATL +
## BAL + CAR + CHI + CIN + CLE + DET + HOU + IND + KC + MIA +
## MINN + NYG + OAK + PHI + PIT + SD + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr +
## grass_1 + bad_weather_1, data = trainTransformed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5044 -0.4254 -0.1184 0.2391 7.5200
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.937e-15 4.841e-03 0.000 1.000000
## weight -6.762e-02 6.073e-03 -11.134 < 2e-16 ***
## cold_weather -1.885e-02 5.015e-03 -3.759 0.000171 ***
## forty1 -4.724e-02 7.051e-03 -6.701 2.11e-11 ***
## ARI 1.569e-02 5.016e-03 3.129 0.001756 **
## ATL 1.962e-02 5.024e-03 3.904 9.47e-05 ***
## BAL 1.819e-02 5.014e-03 3.628 0.000286 ***
## CAR 1.267e-02 5.031e-03 2.518 0.011819 *
## CHI 1.667e-02 5.013e-03 3.324 0.000887 ***
## CIN 1.229e-02 5.007e-03 2.455 0.014086 *
## CLE 2.934e-02 5.054e-03 5.805 6.52e-09 ***
## DET 1.563e-02 5.009e-03 3.121 0.001806 **
## HOU 2.085e-02 5.027e-03 4.149 3.36e-05 ***
## IND 1.087e-02 5.008e-03 2.171 0.029942 *
## KC 1.237e-02 5.058e-03 2.446 0.014468 *
## MIA 1.340e-02 5.010e-03 2.675 0.007469 **
## MINN 1.335e-02 5.013e-03 2.663 0.007741 **
## NYG 1.433e-02 5.010e-03 2.859 0.004248 **
## OAK 1.420e-02 5.072e-03 2.800 0.005108 **
## PHI 1.711e-02 5.008e-03 3.416 0.000636 ***
## PIT 2.404e-02 5.044e-03 4.766 1.89e-06 ***
## SD 1.377e-02 5.042e-03 2.730 0.006333 **
## STL 1.214e-02 5.021e-03 2.417 0.015636 *
## TB 1.037e-02 5.025e-03 2.064 0.039052 *
## TEN 1.028e-02 5.042e-03 2.038 0.041578 *
## WAS 1.921e-02 5.036e-03 3.815 0.000136 ***
## avg_rectd_plyr 5.394e-01 6.049e-03 89.176 < 2e-16 ***
## avg_rbry_plyr 4.649e-02 6.950e-03 6.689 2.29e-11 ***
## avg_rbry_pos -7.193e-02 7.494e-03 -9.600 < 2e-16 ***
## avg_qbtdp_plyr -4.723e-02 5.861e-03 -8.057 8.13e-16 ***
## grass_1 -1.649e-02 5.271e-03 -3.128 0.001760 **
## bad_weather_1 -9.828e-03 4.915e-03 -1.999 0.045573 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8025 on 27452 degrees of freedom
## Multiple R-squared: 0.3567, Adjusted R-squared: 0.356
## F-statistic: 491 on 31 and 27452 DF, p-value: < 2.2e-16Modest gains in r-square and residual standard error and we cut the variables down to just 3. R2 is not very strong 0.4277. This is an improvement (slightly) over the historical average only as the explanatory variable.
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
RecyPredicted <- predict(linRegrecy3, newdata = testTransformed)
SSErecy <- sum((RecyPredicted - testTransformed$recy)^2)
SSTrecy <- sum((mean(nfl_data$recy)-testTransformed$recy)^2)
r2_recy <- 1 - SSErecy/SSTrecy
r2_recy## [1] 0.9989364rmse_recy <- sqrt(SSErecy/nrow(testTransformed))
rmse_recy## [1] 0.7763582Looking at the regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegrecy3, which = c(1,2,3,5))
The residuals vs fitted appears to be okay for the model. The normal Q-Q looks okay, however, it may have some skewness to it. The scale-location does not seem to be ideal. The red line is not smooth, and there appears to be a gap in the data. The residuals vs leverage has some values that seem extreme.
The summary statistics are below.
confint(linRegrecy3)## 2.5 % 97.5 %
## (Intercept) -0.0094882559 0.0094882559
## weight -0.0795274473 -0.0557191232
## cold_weather -0.0286793102 -0.0090208176
## forty1 -0.0610642220 -0.0334250908
## ARI 0.0058632903 0.0255259948
## ATL 0.0097682460 0.0294637762
## BAL 0.0083622071 0.0280189326
## CAR 0.0028054154 0.0225280288
## CHI 0.0068398849 0.0264926557
## CIN 0.0024791450 0.0221055179
## CLE 0.0194316899 0.0392452933
## DET 0.0058143275 0.0254512802
## HOU 0.0110002904 0.0307047052
## IND 0.0010562904 0.0206882581
## KC 0.0024557801 0.0222837058
## MIA 0.0035838450 0.0232233998
## MINN 0.0035260161 0.0231792969
## NYG 0.0045059231 0.0241468691
## OAK 0.0042619829 0.0241443427
## PHI 0.0072919585 0.0269223314
## PIT 0.0141504048 0.0339216782
## SD 0.0038833042 0.0236481674
## STL 0.0022968544 0.0219812473
## TB 0.0005210029 0.0202187408
## TEN 0.0003920961 0.0201581502
## WAS 0.0093422705 0.0290834158
## avg_rectd_plyr 0.5275582024 0.5512702914
## avg_rbry_plyr 0.0328656806 0.0601111735
## avg_rbry_pos -0.0866224971 -0.0572471575
## avg_qbtdp_plyr -0.0587148793 -0.0357375061
## grass_1 -0.0268191284 -0.0061578226
## bad_weather_1 -0.0194620323 -0.0001935083coef(summary(linRegrecy3))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.937290e-15 0.004840822 -6.067751e-13 1.000000e+00
## weight -6.762329e-02 0.006073396 -1.113435e+01 9.837517e-29
## cold_weather -1.885006e-02 0.005014793 -3.758892e+00 1.710209e-04
## forty1 -4.724466e-02 0.007050617 -6.700783e+00 2.113140e-11
## ARI 1.569464e-02 0.005015867 3.128999e+00 1.755866e-03
## ATL 1.961601e-02 0.005024241 3.904274e+00 9.473462e-05
## BAL 1.819057e-02 0.005014342 3.627708e+00 2.864663e-04
## CAR 1.266672e-02 0.005031150 2.517660e+00 1.181939e-02
## CHI 1.666627e-02 0.005013333 3.324389e+00 8.872841e-04
## CIN 1.229233e-02 0.005006599 2.455226e+00 1.408576e-02
## CLE 2.933849e-02 0.005054361 5.804590e+00 6.523318e-09
## DET 1.563280e-02 0.005009298 3.120757e+00 1.805735e-03
## HOU 2.085250e-02 0.005026507 4.148507e+00 3.356579e-05
## IND 1.087227e-02 0.005008026 2.170970e+00 2.994199e-02
## KC 1.236974e-02 0.005058014 2.445573e+00 1.446845e-02
## MIA 1.340362e-02 0.005009962 2.675394e+00 7.468569e-03
## MINN 1.335266e-02 0.005013463 2.663360e+00 7.740977e-03
## NYG 1.432640e-02 0.005010317 2.859379e+00 4.247906e-03
## OAK 1.420316e-02 0.005071900 2.800363e+00 5.108079e-03
## PHI 1.710714e-02 0.005007619 3.416223e+00 6.358817e-04
## PIT 2.403604e-02 0.005043563 4.765687e+00 1.891737e-06
## SD 1.376574e-02 0.005041927 2.730253e+00 6.332615e-03
## STL 1.213905e-02 0.005021400 2.417464e+00 1.563557e-02
## TB 1.036987e-02 0.005024804 2.063737e+00 3.905207e-02
## TEN 1.027512e-02 0.005042231 2.037813e+00 4.157822e-02
## WAS 1.921284e-02 0.005035877 3.815193e+00 1.363745e-04
## avg_rectd_plyr 5.394142e-01 0.006048847 8.917638e+01 0.000000e+00
## avg_rbry_plyr 4.648843e-02 0.006950202 6.688788e+00 2.293467e-11
## avg_rbry_pos -7.193483e-02 0.007493516 -9.599609e+00 8.683028e-22
## avg_qbtdp_plyr -4.722619e-02 0.005861424 -8.057119e+00 8.125991e-16
## grass_1 -1.648848e-02 0.005270606 -3.128383e+00 1.759546e-03
## bad_weather_1 -9.827770e-03 0.004915313 -1.999419e+00 4.557289e-02anova(linRegrecy3)## Analysis of Variance Table
##
## Response: recy
## Df Sum Sq Mean Sq F value Pr(>F)
## weight 1 286.5 286.5 444.7939 < 2.2e-16 ***
## cold_weather 1 17.7 17.7 27.4087 1.659e-07 ***
## forty1 1 1096.0 1096.0 1701.7895 < 2.2e-16 ***
## ARI 1 1.6 1.6 2.4409 0.1182194
## ATL 1 22.2 22.2 34.5178 4.272e-09 ***
## BAL 1 0.0 0.0 0.0026 0.9592773
## CAR 1 3.4 3.4 5.2935 0.0214132 *
## CHI 1 0.0 0.0 0.0001 0.9922825
## CIN 1 0.0 0.0 0.0696 0.7919203
## CLE 1 1.6 1.6 2.4396 0.1183183
## DET 1 13.6 13.6 21.1018 4.375e-06 ***
## HOU 1 0.8 0.8 1.2155 0.2702583
## IND 1 1.2 1.2 1.9041 0.1676280
## KC 1 13.8 13.8 21.3793 3.785e-06 ***
## MIA 1 0.1 0.1 0.1325 0.7158119
## MINN 1 8.8 8.8 13.6466 0.0002211 ***
## NYG 1 7.1 7.1 11.0093 0.0009078 ***
## OAK 1 12.5 12.5 19.3499 1.092e-05 ***
## PHI 1 1.5 1.5 2.3813 0.1228075
## PIT 1 10.1 10.1 15.6244 7.745e-05 ***
## SD 1 8.7 8.7 13.5839 0.0002286 ***
## STL 1 3.6 3.6 5.6376 0.0175859 *
## TB 1 0.9 0.9 1.3868 0.2389488
## TEN 1 6.5 6.5 10.0632 0.0015142 **
## WAS 1 2.1 2.1 3.2224 0.0726498 .
## avg_rectd_plyr 1 8183.3 8183.3 12705.9907 < 2.2e-16 ***
## avg_rbry_plyr 1 0.1 0.1 0.2085 0.6479341
## avg_rbry_pos 1 47.9 47.9 74.4186 < 2.2e-16 ***
## avg_qbtdp_plyr 1 42.0 42.0 65.1375 7.268e-16 ***
## grass_1 1 6.5 6.5 10.1376 0.0014544 **
## bad_weather_1 1 2.6 2.6 3.9977 0.0455729 *
## Residuals 27452 17680.4 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1I would say overall, the model is just okay for predicting. The average yards receiving historical for the player is really the best predictor according to this analysis
Now we inspect the AIC:
#aic
aic_recy <- step(lm(wrrecyregform, data = trainTransformed), direction = "backward")## Start: AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.0 17665 -12058.4
## - GB 1 0.0 17665 -12058.4
## - height 1 0.1 17665 -12058.2
## - vertical1 1 0.1 17665 -12058.2
## - home_team_1 1 0.5 17666 -12057.6
## - avg_fuml_plyr 1 0.6 17666 -12057.4
## - hot_weather 1 1.0 17666 -12056.8
## <none> 17665 -12056.4
## - BUF 1 1.4 17666 -12056.2
## - DEN 1 1.6 17667 -12056.0
## - NOR 1 2.2 17667 -12055.0
## - DAL 1 2.2 17667 -12054.9
## - bad_weather_1 1 2.4 17667 -12054.6
## - NYJ 1 2.5 17668 -12054.4
## - JAC 1 3.7 17669 -12052.6
## - NE 1 3.8 17669 -12052.5
## - grass_1 1 3.9 17669 -12052.4
## - TEN 1 5.1 17670 -12050.4
## - IND 1 5.2 17670 -12050.2
## - TB 1 5.4 17671 -12049.9
## - KC 1 6.1 17671 -12048.8
## - STL 1 6.2 17671 -12048.8
## - CIN 1 6.4 17671 -12048.5
## - CAR 1 6.5 17672 -12048.3
## - MINN 1 6.8 17672 -12047.8
## - MIA 1 7.1 17672 -12047.4
## - OAK 1 7.2 17672 -12047.2
## - SD 1 7.4 17672 -12046.9
## - NYG 1 7.7 17673 -12046.4
## - cold_weather 1 7.8 17673 -12046.2
## - ARI 1 8.1 17673 -12045.8
## - DET 1 8.3 17673 -12045.5
## - CHI 1 9.2 17674 -12044.1
## - PHI 1 9.7 17675 -12043.2
## - BAL 1 10.2 17675 -12042.5
## - ATL 1 10.9 17676 -12041.4
## - WAS 1 11.2 17676 -12040.9
## - HOU 1 11.7 17677 -12040.2
## - PIT 1 15.1 17680 -12034.8
## - avg_qbtdp_plyr 1 19.8 17685 -12027.5
## - forty1 1 20.5 17686 -12026.5
## - CLE 1 20.5 17686 -12026.5
## - avg_rbry_plyr 1 28.9 17694 -12013.4
## - weight 1 40.5 17706 -11995.5
## - avg_rbry_pos 1 44.0 17709 -11990.1
## - avg_rectd_plyr 1 4892.2 22557 -5339.4
##
## Step: AIC=-12058.36
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - GB 1 0.0 17665 -12060.4
## - height 1 0.1 17665 -12060.2
## - vertical1 1 0.1 17665 -12060.2
## - home_team_1 1 0.5 17666 -12059.6
## - avg_fuml_plyr 1 0.6 17666 -12059.4
## - hot_weather 1 1.1 17666 -12058.7
## <none> 17665 -12058.4
## - BUF 1 2.1 17667 -12057.1
## - DEN 1 2.3 17667 -12056.8
## - bad_weather_1 1 2.4 17668 -12056.6
## - DAL 1 3.2 17668 -12055.4
## - NOR 1 3.2 17668 -12055.4
## - NYJ 1 3.7 17669 -12054.6
## - grass_1 1 3.9 17669 -12054.4
## - JAC 1 5.1 17670 -12052.4
## - NE 1 5.4 17671 -12051.9
## - TEN 1 7.1 17672 -12049.4
## - IND 1 7.4 17672 -12048.9
## - TB 1 7.5 17673 -12048.7
## - cold_weather 1 7.9 17673 -12048.0
## - KC 1 8.5 17674 -12047.1
## - STL 1 8.5 17674 -12047.1
## - CAR 1 8.9 17674 -12046.5
## - CIN 1 8.9 17674 -12046.4
## - MINN 1 9.5 17675 -12045.6
## - MIA 1 9.7 17675 -12045.3
## - OAK 1 9.9 17675 -12045.0
## - SD 1 10.0 17675 -12044.8
## - NYG 1 10.8 17676 -12043.5
## - ARI 1 11.2 17676 -12042.9
## - DET 1 11.4 17677 -12042.6
## - CHI 1 12.5 17678 -12041.0
## - PHI 1 13.2 17678 -12039.8
## - BAL 1 14.4 17680 -12037.9
## - ATL 1 15.1 17680 -12036.9
## - WAS 1 15.4 17681 -12036.4
## - HOU 1 16.1 17681 -12035.3
## - avg_qbtdp_plyr 1 19.9 17685 -12029.5
## - forty1 1 20.5 17686 -12028.5
## - PIT 1 20.8 17686 -12028.0
## - CLE 1 27.7 17693 -12017.2
## - avg_rbry_plyr 1 28.9 17694 -12015.4
## - weight 1 40.5 17706 -11997.4
## - avg_rbry_pos 1 44.0 17709 -11992.1
## - avg_rectd_plyr 1 4892.2 22557 -5341.4
##
## Step: AIC=-12060.35
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + HOU + IND + JAC + KC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - height 1 0.1 17665 -12062.2
## - vertical1 1 0.1 17665 -12062.2
## - home_team_1 1 0.5 17666 -12061.6
## - avg_fuml_plyr 1 0.6 17666 -12061.4
## - hot_weather 1 1.1 17666 -12060.7
## <none> 17665 -12060.4
## - BUF 1 2.4 17668 -12058.6
## - bad_weather_1 1 2.4 17668 -12058.6
## - DEN 1 2.7 17668 -12058.2
## - DAL 1 3.7 17669 -12056.6
## - NOR 1 3.7 17669 -12056.5
## - grass_1 1 3.9 17669 -12056.3
## - NYJ 1 4.2 17669 -12055.8
## - JAC 1 5.9 17671 -12053.2
## - NE 1 6.3 17671 -12052.5
## - cold_weather 1 8.0 17673 -12049.9
## - TEN 1 8.1 17673 -12049.8
## - IND 1 8.4 17674 -12049.3
## - TB 1 8.6 17674 -12049.0
## - STL 1 9.6 17675 -12047.4
## - KC 1 9.8 17675 -12047.1
## - CIN 1 10.2 17675 -12046.5
## - CAR 1 10.2 17675 -12046.5
## - MINN 1 10.7 17676 -12045.7
## - MIA 1 11.1 17676 -12045.1
## - OAK 1 11.3 17676 -12044.7
## - SD 1 11.5 17677 -12044.5
## - NYG 1 12.4 17677 -12043.1
## - ARI 1 12.7 17678 -12042.6
## - DET 1 12.9 17678 -12042.2
## - CHI 1 14.2 17679 -12040.3
## - PHI 1 15.0 17680 -12039.0
## - BAL 1 16.5 17682 -12036.7
## - ATL 1 17.1 17682 -12035.8
## - WAS 1 17.6 17683 -12035.0
## - HOU 1 18.2 17683 -12034.0
## - avg_qbtdp_plyr 1 19.9 17685 -12031.4
## - forty1 1 20.5 17686 -12030.4
## - PIT 1 23.9 17689 -12025.2
## - avg_rbry_plyr 1 28.9 17694 -12017.4
## - CLE 1 31.4 17697 -12013.5
## - weight 1 40.5 17706 -11999.4
## - avg_rbry_pos 1 44.0 17709 -11993.9
## - avg_rectd_plyr 1 4928.2 22593 -5299.6
##
## Step: AIC=-12062.19
## recy ~ weight + cold_weather + hot_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 0.1 17665 -12064.0
## - home_team_1 1 0.5 17666 -12063.4
## - avg_fuml_plyr 1 0.6 17666 -12063.3
## - hot_weather 1 1.1 17666 -12062.5
## <none> 17665 -12062.2
## - bad_weather_1 1 2.4 17668 -12060.4
## - BUF 1 2.5 17668 -12060.3
## - DEN 1 2.7 17668 -12060.0
## - DAL 1 3.7 17669 -12058.4
## - NOR 1 3.8 17669 -12058.3
## - grass_1 1 3.9 17669 -12058.1
## - NYJ 1 4.3 17669 -12057.5
## - JAC 1 5.9 17671 -12055.0
## - NE 1 6.3 17671 -12054.4
## - cold_weather 1 8.0 17673 -12051.7
## - TEN 1 8.2 17673 -12051.5
## - IND 1 8.4 17674 -12051.1
## - TB 1 8.6 17674 -12050.8
## - STL 1 9.7 17675 -12049.1
## - KC 1 9.9 17675 -12048.8
## - CAR 1 10.2 17675 -12048.3
## - CIN 1 10.3 17676 -12048.1
## - MINN 1 10.9 17676 -12047.2
## - MIA 1 11.2 17676 -12046.8
## - SD 1 11.6 17677 -12046.1
## - OAK 1 11.7 17677 -12046.0
## - NYG 1 12.5 17678 -12044.8
## - ARI 1 12.9 17678 -12044.2
## - DET 1 13.0 17678 -12044.0
## - CHI 1 14.5 17680 -12041.7
## - PHI 1 15.1 17680 -12040.8
## - BAL 1 16.6 17682 -12038.4
## - ATL 1 17.1 17682 -12037.6
## - WAS 1 17.5 17683 -12037.0
## - HOU 1 18.5 17684 -12035.5
## - forty1 1 20.5 17686 -12032.3
## - avg_qbtdp_plyr 1 20.6 17686 -12032.2
## - PIT 1 24.0 17689 -12026.9
## - avg_rbry_plyr 1 29.0 17694 -12019.1
## - CLE 1 31.6 17697 -12015.1
## - avg_rbry_pos 1 60.4 17726 -11970.3
## - weight 1 76.5 17742 -11945.5
## - avg_rectd_plyr 1 4988.4 22654 -5228.3
##
## Step: AIC=-12064
## recy ~ weight + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - home_team_1 1 0.5 17666 -12065.2
## - avg_fuml_plyr 1 0.6 17666 -12065.1
## - hot_weather 1 1.1 17666 -12064.4
## <none> 17665 -12064.0
## - bad_weather_1 1 2.4 17668 -12062.3
## - BUF 1 2.4 17668 -12062.2
## - DEN 1 2.7 17668 -12061.8
## - DAL 1 3.7 17669 -12060.2
## - NOR 1 3.8 17669 -12060.1
## - grass_1 1 3.9 17669 -12059.9
## - NYJ 1 4.4 17670 -12059.2
## - JAC 1 6.0 17671 -12056.6
## - NE 1 6.3 17672 -12056.2
## - cold_weather 1 8.0 17673 -12053.5
## - TEN 1 8.2 17674 -12053.2
## - IND 1 8.5 17674 -12052.9
## - TB 1 8.6 17674 -12052.6
## - STL 1 9.7 17675 -12050.9
## - KC 1 9.9 17675 -12050.6
## - CAR 1 10.3 17676 -12050.0
## - CIN 1 10.3 17676 -12050.0
## - MINN 1 11.1 17676 -12048.8
## - MIA 1 11.1 17676 -12048.7
## - OAK 1 11.6 17677 -12047.9
## - SD 1 11.6 17677 -12047.9
## - NYG 1 12.5 17678 -12046.6
## - ARI 1 12.8 17678 -12046.0
## - DET 1 13.1 17678 -12045.6
## - CHI 1 14.4 17680 -12043.6
## - PHI 1 15.0 17680 -12042.7
## - BAL 1 16.6 17682 -12040.3
## - ATL 1 17.0 17682 -12039.6
## - WAS 1 17.5 17683 -12038.8
## - HOU 1 18.6 17684 -12037.1
## - avg_qbtdp_plyr 1 20.6 17686 -12034.0
## - PIT 1 24.0 17689 -12028.7
## - avg_rbry_plyr 1 28.9 17694 -12021.1
## - forty1 1 30.5 17696 -12018.6
## - CLE 1 31.8 17697 -12016.6
## - avg_rbry_pos 1 60.7 17726 -11971.7
## - weight 1 76.9 17742 -11946.6
## - avg_rectd_plyr 1 5002.4 22668 -5213.2
##
## Step: AIC=-12065.24
## recy ~ weight + cold_weather + hot_weather + forty1 + ARI + ATL +
## BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU +
## IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_fuml_plyr 1 0.6 17666 -12066.3
## - hot_weather 1 1.0 17667 -12065.6
## <none> 17666 -12065.2
## - BUF 1 2.4 17668 -12063.4
## - bad_weather_1 1 2.5 17668 -12063.4
## - DEN 1 2.7 17669 -12063.0
## - NOR 1 4.0 17670 -12061.0
## - DAL 1 4.2 17670 -12060.8
## - NYJ 1 4.3 17670 -12060.5
## - grass_1 1 4.4 17670 -12060.3
## - JAC 1 6.0 17672 -12057.9
## - NE 1 6.2 17672 -12057.6
## - TEN 1 8.2 17674 -12054.4
## - cold_weather 1 8.3 17674 -12054.3
## - TB 1 8.6 17674 -12053.9
## - IND 1 9.0 17675 -12053.2
## - KC 1 9.9 17676 -12051.8
## - CIN 1 10.3 17676 -12051.3
## - CAR 1 10.3 17676 -12051.3
## - STL 1 10.3 17676 -12051.2
## - MINN 1 11.1 17677 -12049.9
## - MIA 1 11.1 17677 -12049.9
## - SD 1 11.7 17677 -12049.1
## - OAK 1 11.7 17678 -12049.1
## - NYG 1 12.4 17678 -12047.9
## - DET 1 13.7 17680 -12045.9
## - ARI 1 13.8 17680 -12045.8
## - CHI 1 14.4 17680 -12044.8
## - PHI 1 15.0 17681 -12043.8
## - BAL 1 16.5 17682 -12041.6
## - WAS 1 17.5 17683 -12040.0
## - ATL 1 18.1 17684 -12039.1
## - HOU 1 19.8 17686 -12036.5
## - avg_qbtdp_plyr 1 20.6 17686 -12035.3
## - PIT 1 24.0 17690 -12029.9
## - avg_rbry_plyr 1 28.9 17695 -12022.3
## - forty1 1 30.4 17696 -12019.9
## - CLE 1 31.8 17698 -12017.8
## - avg_rbry_pos 1 60.7 17727 -11973.0
## - weight 1 76.9 17743 -11947.8
## - avg_rectd_plyr 1 5002.6 22668 -5214.3
##
## Step: AIC=-12066.32
## recy ~ weight + cold_weather + hot_weather + forty1 + ARI + ATL +
## BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU +
## IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 1.0 17667 -12066.7
## <none> 17666 -12066.3
## - BUF 1 2.3 17669 -12064.7
## - bad_weather_1 1 2.4 17669 -12064.5
## - DEN 1 2.6 17669 -12064.2
## - NOR 1 4.0 17670 -12062.0
## - DAL 1 4.1 17671 -12061.9
## - NYJ 1 4.2 17671 -12061.8
## - grass_1 1 4.4 17671 -12061.4
## - JAC 1 6.0 17672 -12059.0
## - NE 1 6.4 17673 -12058.4
## - TEN 1 8.0 17674 -12055.8
## - cold_weather 1 8.2 17675 -12055.5
## - TB 1 8.4 17675 -12055.2
## - IND 1 8.9 17675 -12054.5
## - KC 1 9.8 17676 -12053.0
## - STL 1 10.1 17677 -12052.6
## - CIN 1 10.1 17677 -12052.5
## - CAR 1 10.1 17677 -12052.5
## - MIA 1 10.9 17677 -12051.3
## - MINN 1 11.0 17677 -12051.2
## - SD 1 11.5 17678 -12050.4
## - OAK 1 11.6 17678 -12050.3
## - NYG 1 12.2 17679 -12049.3
## - DET 1 13.5 17680 -12047.4
## - ARI 1 13.5 17680 -12047.3
## - CHI 1 14.1 17681 -12046.3
## - PHI 1 14.7 17681 -12045.4
## - BAL 1 16.4 17683 -12042.7
## - WAS 1 17.2 17684 -12041.6
## - ATL 1 18.2 17685 -12040.0
## - HOU 1 19.7 17686 -12037.7
## - PIT 1 23.8 17690 -12031.4
## - avg_rbry_plyr 1 29.5 17696 -12022.5
## - forty1 1 30.6 17697 -12020.7
## - CLE 1 31.4 17698 -12019.5
## - avg_qbtdp_plyr 1 40.9 17707 -12004.8
## - avg_rbry_pos 1 60.6 17727 -11974.2
## - weight 1 76.3 17743 -11949.8
## - avg_rectd_plyr 1 5004.1 22671 -5213.8
##
## Step: AIC=-12066.69
## recy ~ weight + cold_weather + forty1 + ARI + ATL + BAL + BUF +
## CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU + IND + JAC +
## KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT +
## SD + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## <none> 17667 -12067
## - BUF 1 2.3 17670 -12065
## - bad_weather_1 1 2.4 17670 -12065
## - DEN 1 2.6 17670 -12065
## - NOR 1 4.0 17671 -12062
## - NYJ 1 4.1 17672 -12062
## - DAL 1 4.2 17672 -12062
## - grass_1 1 4.7 17672 -12061
## - JAC 1 6.1 17674 -12059
## - NE 1 6.4 17674 -12059
## - cold_weather 1 8.0 17675 -12056
## - TEN 1 8.2 17676 -12056
## - TB 1 8.3 17676 -12056
## - IND 1 9.0 17676 -12055
## - KC 1 10.0 17677 -12053
## - STL 1 10.0 17677 -12053
## - CIN 1 10.2 17678 -12053
## - CAR 1 10.3 17678 -12053
## - MINN 1 11.1 17679 -12052
## - MIA 1 11.1 17679 -12052
## - SD 1 11.3 17679 -12051
## - OAK 1 11.8 17679 -12050
## - NYG 1 12.3 17680 -12050
## - DET 1 13.6 17681 -12048
## - ARI 1 13.6 17681 -12048
## - CHI 1 14.3 17682 -12046
## - PHI 1 14.9 17682 -12046
## - BAL 1 16.5 17684 -12043
## - WAS 1 17.4 17685 -12042
## - ATL 1 18.3 17686 -12040
## - HOU 1 19.8 17687 -12038
## - PIT 1 23.7 17691 -12032
## - avg_rbry_plyr 1 29.4 17697 -12023
## - forty1 1 30.6 17698 -12021
## - CLE 1 31.6 17699 -12020
## - avg_qbtdp_plyr 1 40.9 17708 -12005
## - avg_rbry_pos 1 60.5 17728 -11975
## - weight 1 76.2 17744 -11950
## - avg_rectd_plyr 1 5004.5 22672 -5214AIC appeared to be very similar to linear regression
Receptions
Preprocess:
set.seed(123)
splitrec <- sample.split(nfl_data$rec, SplitRatio = 0.7)
TrainRec <- subset(nfl_data, split == TRUE)
TestRec <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(TrainRec, method = c("center", "scale"))
trainTransformedrec <- predict(preProcValues, TrainRec)
testTransformedrec <- predict(preProcValues, TestRec)ggpairs:
ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[46:51]))])
####Regressions
recregform <- formula(paste("rec ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegrec <- lm(recregform, data = trainTransformedrec)
summary(linRegrec)##
## Call:
## lm(formula = recregform, data = trainTransformedrec)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3983 -0.5040 -0.1305 0.3285 6.4639
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.263e-15 4.892e-03 0.000 1.000000
## height -5.461e-02 9.491e-03 -5.754 8.80e-09 ***
## weight -2.440e-02 8.895e-03 -2.743 0.006086 **
## cold_weather -1.923e-02 5.149e-03 -3.735 0.000188 ***
## hot_weather -6.469e-03 4.937e-03 -1.310 0.190046
## home_team_1 -1.158e-02 5.323e-03 -2.176 0.029552 *
## forty1 -1.172e-02 8.442e-03 -1.388 0.165044
## vertical1 -8.435e-03 6.491e-03 -1.299 0.193796
## ARI 3.153e-02 6.843e-03 4.608 4.08e-06 ***
## ATL 4.264e-02 6.876e-03 6.201 5.69e-10 ***
## BAL 4.300e-02 6.882e-03 6.248 4.21e-10 ***
## BUF 2.455e-02 6.793e-03 3.614 0.000302 ***
## CAR 2.053e-02 6.749e-03 3.042 0.002349 **
## CHI 3.920e-02 6.673e-03 5.874 4.30e-09 ***
## CIN 3.801e-02 6.796e-03 5.593 2.26e-08 ***
## CLE 5.026e-02 6.765e-03 7.429 1.13e-13 ***
## DAL 2.544e-02 6.834e-03 3.722 0.000198 ***
## DEN 2.065e-02 6.860e-03 3.011 0.002610 **
## DET 4.279e-02 6.765e-03 6.325 2.57e-10 ***
## GB 1.068e-02 6.965e-03 1.533 0.125309
## HOU 4.230e-02 6.882e-03 6.147 8.02e-10 ***
## IND 3.629e-02 6.832e-03 5.312 1.10e-07 ***
## JAC 3.418e-02 6.664e-03 5.129 2.93e-07 ***
## KC 3.732e-02 6.810e-03 5.480 4.29e-08 ***
## MIA 3.389e-02 6.700e-03 5.058 4.27e-07 ***
## MINN 4.262e-02 6.741e-03 6.323 2.61e-10 ***
## NE 2.320e-02 7.041e-03 3.295 0.000987 ***
## NOR 3.709e-02 7.019e-03 5.284 1.28e-07 ***
## NYG 3.193e-02 6.861e-03 4.655 3.26e-06 ***
## NYJ 2.036e-02 6.835e-03 2.979 0.002899 **
## OAK 3.707e-02 6.878e-03 5.389 7.15e-08 ***
## PHI 3.422e-02 6.665e-03 5.135 2.85e-07 ***
## PIT 4.368e-02 6.840e-03 6.385 1.74e-10 ***
## SD 3.523e-02 6.712e-03 5.248 1.55e-07 ***
## SEA 5.694e-03 6.966e-03 0.817 0.413725
## STL 3.416e-02 6.780e-03 5.038 4.73e-07 ***
## TB 2.219e-02 6.717e-03 3.303 0.000957 ***
## TEN 2.769e-02 6.757e-03 4.097 4.20e-05 ***
## WAS 3.684e-02 6.793e-03 5.424 5.89e-08 ***
## avg_trg_team NA NA NA NA
## avg_rectd_plyr 5.405e-01 6.247e-03 86.520 < 2e-16 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr 1.298e-01 7.476e-03 17.365 < 2e-16 ***
## avg_rbry_pos -7.565e-02 8.711e-03 -8.685 < 2e-16 ***
## avg_fuml_plyr -6.774e-03 7.226e-03 -0.937 0.348541
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -9.907e-02 7.849e-03 -12.621 < 2e-16 ***
## avg_qbtdp_team NA NA NA NA
## grass_1 -1.219e-02 5.628e-03 -2.166 0.030352 *
## bad_weather_1 -1.059e-02 4.976e-03 -2.127 0.033423 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.811 on 27438 degrees of freedom
## Multiple R-squared: 0.3434, Adjusted R-squared: 0.3423
## F-statistic: 318.8 on 45 and 27438 DF, p-value: < 2.2e-16linRegrec2 <- update(linRegrec, ~. -hot_weather -forty1 -GB - SEA -avg_trg_team -avg_tdr_team
-avg_rbra_team -avg_fuml_team -avg_qbtdp_team - avg_qbints_team)
summary(linRegrec2)##
## Call:
## lm(formula = rec ~ height + weight + cold_weather + home_team_1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1, data = trainTransformedrec)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4209 -0.5034 -0.1309 0.3328 6.4705
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.117e-15 4.892e-03 0.000 1.000000
## height -5.471e-02 9.491e-03 -5.764 8.30e-09 ***
## weight -2.930e-02 8.141e-03 -3.599 0.000320 ***
## cold_weather -1.831e-02 5.123e-03 -3.575 0.000351 ***
## home_team_1 -1.155e-02 5.322e-03 -2.171 0.029960 *
## vertical1 -4.085e-03 5.539e-03 -0.737 0.460839
## ARI 2.666e-02 5.614e-03 4.749 2.05e-06 ***
## ATL 3.730e-02 5.633e-03 6.623 3.59e-11 ***
## BAL 3.765e-02 5.566e-03 6.765 1.36e-11 ***
## BUF 1.944e-02 5.550e-03 3.503 0.000460 ***
## CAR 1.562e-02 5.537e-03 2.820 0.004799 **
## CHI 3.435e-02 5.517e-03 6.226 4.85e-10 ***
## CIN 3.262e-02 5.545e-03 5.883 4.07e-09 ***
## CLE 4.498e-02 5.565e-03 8.084 6.53e-16 ***
## DAL 2.017e-02 5.601e-03 3.601 0.000317 ***
## DEN 1.502e-02 5.578e-03 2.693 0.007076 **
## DET 3.750e-02 5.571e-03 6.733 1.70e-11 ***
## HOU 3.675e-02 5.638e-03 6.517 7.28e-11 ***
## IND 3.111e-02 5.584e-03 5.571 2.56e-08 ***
## JAC 2.900e-02 5.522e-03 5.251 1.52e-07 ***
## KC 3.215e-02 5.575e-03 5.767 8.16e-09 ***
## MIA 2.886e-02 5.521e-03 5.227 1.73e-07 ***
## MINN 3.747e-02 5.549e-03 6.752 1.49e-11 ***
## NE 1.674e-02 5.633e-03 2.971 0.002969 **
## NOR 3.146e-02 5.652e-03 5.566 2.64e-08 ***
## NYG 2.637e-02 5.564e-03 4.741 2.14e-06 ***
## NYJ 1.466e-02 5.568e-03 2.632 0.008481 **
## OAK 3.227e-02 5.625e-03 5.737 9.74e-09 ***
## PHI 2.928e-02 5.505e-03 5.319 1.05e-07 ***
## PIT 3.819e-02 5.564e-03 6.863 6.89e-12 ***
## SD 2.956e-02 5.545e-03 5.331 9.86e-08 ***
## STL 2.873e-02 5.595e-03 5.135 2.85e-07 ***
## TB 1.688e-02 5.539e-03 3.048 0.002303 **
## TEN 2.255e-02 5.564e-03 4.052 5.08e-05 ***
## WAS 3.198e-02 5.557e-03 5.755 8.73e-09 ***
## avg_rectd_plyr 5.423e-01 6.172e-03 87.875 < 2e-16 ***
## avg_rbry_plyr 1.315e-01 7.367e-03 17.849 < 2e-16 ***
## avg_rbry_pos -7.500e-02 8.704e-03 -8.617 < 2e-16 ***
## avg_fuml_plyr -7.142e-03 7.223e-03 -0.989 0.322784
## avg_qbtdp_plyr -1.016e-01 7.524e-03 -13.506 < 2e-16 ***
## grass_1 -1.263e-02 5.550e-03 -2.275 0.022914 *
## bad_weather_1 -1.047e-02 4.976e-03 -2.104 0.035390 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.811 on 27442 degrees of freedom
## Multiple R-squared: 0.3432, Adjusted R-squared: 0.3422
## F-statistic: 349.8 on 41 and 27442 DF, p-value: < 2.2e-16We had a modest r-square improvement. The R2 is not very strong (0.4457), and we achieved approximately the same value when we cut the variables down to just 6. Much simpler model with similar results
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
RecPredicted <- predict(linRegrec2, newdata = testTransformedrec)
SSErec <- sum((RecPredicted - testTransformedrec$rec)^2)
SSTrec <- sum((mean(nfl_data$rec)-testTransformedrec$rec)^2)
r2_rec <- 1 - SSErec/SSTrec
r2_rec## [1] 0.8782749rmse_rec <- sqrt(SSErec/nrow(testTransformedrec))
rmse_rec## [1] 0.7969974Looking at the regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegrec2, which = c(1,2,3,5))
The charts show very similarly to what we saw above for receiving yards.
The summary statistics are below:
confint(linRegrec2)## 2.5 % 97.5 %
## (Intercept) -0.009588716 0.0095887159
## height -0.073311748 -0.0361050567
## weight -0.045255501 -0.0133437044
## cold_weather -0.028355199 -0.0082735662
## home_team_1 -0.021982346 -0.0011211872
## vertical1 -0.014940648 0.0067714074
## ARI 0.015659421 0.0376682885
## ATL 0.026264525 0.0483453015
## BAL 0.026742150 0.0485595637
## BUF 0.008565760 0.0303229949
## CAR 0.004764205 0.0264702673
## CHI 0.023535464 0.0451622569
## CIN 0.021751469 0.0434865873
## CLE 0.034077046 0.0558912642
## DAL 0.009192547 0.0311496124
## DEN 0.004090978 0.0259579177
## DET 0.026585238 0.0484223772
## HOU 0.025694103 0.0477960158
## IND 0.020163375 0.0420543502
## JAC 0.018173687 0.0398186007
## KC 0.021223060 0.0430769410
## MIA 0.018036876 0.0396783173
## MINN 0.026591036 0.0483440036
## NE 0.005695593 0.0277778225
## NOR 0.020379366 0.0425360434
## NYG 0.015470120 0.0372797756
## NYJ 0.003744224 0.0255720611
## OAK 0.021246695 0.0432984222
## PHI 0.018488304 0.0400684540
## PIT 0.027280183 0.0490917161
## SD 0.018690394 0.0404276600
## STL 0.017761430 0.0396942051
## TB 0.006028188 0.0277415125
## TEN 0.011642942 0.0334557042
## WAS 0.021089472 0.0428718167
## avg_rectd_plyr 0.530241430 0.5544352471
## avg_rbry_plyr 0.117052640 0.1459311941
## avg_rbry_pos -0.092064124 -0.0579440215
## avg_fuml_plyr -0.021300372 0.0070158912
## avg_qbtdp_plyr -0.116366581 -0.0868717574
## grass_1 -0.023503224 -0.0017478469
## bad_weather_1 -0.020222651 -0.0007161738coef(summary(linRegrec2))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.117011e-15 0.004892076 -8.415672e-13 1.000000e+00
## height -5.470840e-02 0.009491259 -5.764083e+00 8.298176e-09
## weight -2.929960e-02 0.008140555 -3.599214e+00 3.197418e-04
## cold_weather -1.831438e-02 0.005122734 -3.575119e+00 3.506695e-04
## home_team_1 -1.155177e-02 0.005321587 -2.170737e+00 2.995960e-02
## vertical1 -4.084620e-03 0.005538647 -7.374762e-01 4.608391e-01
## ARI 2.666385e-02 0.005614363 4.749222e+00 2.052317e-06
## ATL 3.730491e-02 0.005632706 6.622911e+00 3.586973e-11
## BAL 3.765086e-02 0.005565523 6.765016e+00 1.359713e-11
## BUF 1.944438e-02 0.005550172 3.503383e+00 4.601199e-04
## CAR 1.561724e-02 0.005537118 2.820463e+00 4.798883e-03
## CHI 3.434886e-02 0.005516897 6.226120e+00 4.850519e-10
## CIN 3.261903e-02 0.005544530 5.883100e+00 4.073201e-09
## CLE 4.498416e-02 0.005564708 8.083830e+00 6.532687e-16
## DAL 2.017108e-02 0.005601148 3.601240e+00 3.172614e-04
## DEN 1.502445e-02 0.005578157 2.693443e+00 7.076126e-03
## DET 3.750381e-02 0.005570555 6.732508e+00 1.700495e-11
## HOU 3.674506e-02 0.005638098 6.517279e+00 7.283502e-11
## IND 3.110886e-02 0.005584289 5.570783e+00 2.559725e-08
## JAC 2.899614e-02 0.005521520 5.251479e+00 1.520063e-07
## KC 3.215000e-02 0.005574826 5.766996e+00 8.156229e-09
## MIA 2.885760e-02 0.005520634 5.227225e+00 1.733312e-07
## MINN 3.746752e-02 0.005549084 6.752019e+00 1.487078e-11
## NE 1.673671e-02 0.005633077 2.971149e+00 2.969453e-03
## NOR 3.145770e-02 0.005652068 5.565698e+00 2.635426e-08
## NYG 2.637495e-02 0.005563544 4.740674e+00 2.140769e-06
## NYJ 1.465814e-02 0.005568182 2.632482e+00 8.481086e-03
## OAK 3.227256e-02 0.005625296 5.737042e+00 9.735669e-09
## PHI 2.927838e-02 0.005504999 5.318508e+00 1.054402e-07
## PIT 3.818595e-02 0.005564024 6.863010e+00 6.885796e-12
## SD 2.955903e-02 0.005545078 5.330678e+00 9.861900e-08
## STL 2.872782e-02 0.005594952 5.134596e+00 2.846801e-07
## TB 1.688485e-02 0.005538971 3.048373e+00 2.303029e-03
## TEN 2.254932e-02 0.005564337 4.052473e+00 5.081867e-05
## WAS 3.198064e-02 0.005556578 5.755457e+00 8.732710e-09
## avg_rectd_plyr 5.423383e-01 0.006171733 8.787456e+01 0.000000e+00
## avg_rbry_plyr 1.314919e-01 0.007366788 1.784929e+01 7.370893e-71
## avg_rbry_pos -7.500407e-02 0.008703884 -8.617311e+00 7.216658e-18
## avg_fuml_plyr -7.142240e-03 0.007223351 -9.887711e-01 3.227839e-01
## avg_qbtdp_plyr -1.016192e-01 0.007523996 -1.350601e+01 1.955406e-41
## grass_1 -1.262554e-02 0.005549698 -2.274995e+00 2.291391e-02
## bad_weather_1 -1.046941e-02 0.004976014 -2.103976e+00 3.538965e-02anova(linRegrec2)## Analysis of Variance Table
##
## Response: rec
## Df Sum Sq Mean Sq F value Pr(>F)
## height 1 0.2 0.2 0.3588 0.5491700
## weight 1 326.5 326.5 496.4268 < 2.2e-16 ***
## cold_weather 1 20.0 20.0 30.4066 3.535e-08 ***
## home_team_1 1 12.3 12.3 18.7076 1.529e-05 ***
## vertical1 1 748.4 748.4 1137.8367 < 2.2e-16 ***
## ARI 1 3.5 3.5 5.2794 0.0215870 *
## ATL 1 36.6 36.6 55.6655 8.846e-14 ***
## BAL 1 0.6 0.6 0.9800 0.3222059
## BUF 1 2.2 2.2 3.3080 0.0689538 .
## CAR 1 8.1 8.1 12.3639 0.0004384 ***
## CHI 1 0.5 0.5 0.8096 0.3682460
## CIN 1 0.2 0.2 0.3079 0.5789480
## CLE 1 3.9 3.9 5.9089 0.0150710 *
## DAL 1 4.1 4.1 6.2492 0.0124309 *
## DEN 1 0.3 0.3 0.3959 0.5292150
## DET 1 12.9 12.9 19.6460 9.356e-06 ***
## HOU 1 0.1 0.1 0.0928 0.7606060
## IND 1 2.3 2.3 3.4616 0.0628218 .
## JAC 1 3.2 3.2 4.9407 0.0262397 *
## KC 1 4.3 4.3 6.4946 0.0108256 *
## MIA 1 1.2 1.2 1.7795 0.1822205
## MINN 1 6.7 6.7 10.1983 0.0014073 **
## NE 1 47.7 47.7 72.5198 < 2.2e-16 ***
## NOR 1 32.1 32.1 48.7564 2.964e-12 ***
## NYG 1 6.3 6.3 9.5470 0.0020048 **
## NYJ 1 13.5 13.5 20.4518 6.141e-06 ***
## OAK 1 3.6 3.6 5.4105 0.0200235 *
## PHI 1 7.7 7.7 11.7561 0.0006073 ***
## PIT 1 18.4 18.4 27.9729 1.240e-07 ***
## SD 1 13.8 13.8 21.0393 4.520e-06 ***
## STL 1 0.0 0.0 0.0049 0.9444320
## TB 1 0.1 0.1 0.1522 0.6964744
## TEN 1 5.5 5.5 8.2967 0.0039749 **
## WAS 1 1.6 1.6 2.4295 0.1190812
## avg_rectd_plyr 1 7645.2 7645.2 11623.1297 < 2.2e-16 ***
## avg_rbry_plyr 1 159.2 159.2 242.0776 < 2.2e-16 ***
## avg_rbry_pos 1 62.5 62.5 95.0615 < 2.2e-16 ***
## avg_fuml_plyr 1 90.7 90.7 137.8181 < 2.2e-16 ***
## avg_qbtdp_plyr 1 120.3 120.3 182.8737 < 2.2e-16 ***
## grass_1 1 3.6 3.6 5.4809 0.0192327 *
## bad_weather_1 1 2.9 2.9 4.4267 0.0353896 *
## Residuals 27442 18050.2 0.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Like the model above, linear regression may not be the best predictor for this statistic
AIC:
aic_rec <- step(lm(recregform, data = TrainRecy), direction = "backward")## Start: AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 2.3 95046 34191
## - avg_fuml_plyr 1 3.0 95046 34191
## - vertical1 1 5.8 95049 34192
## - hot_weather 1 5.9 95049 34192
## - forty1 1 6.7 95050 34192
## <none> 95043 34192
## - GB 1 8.1 95052 34193
## - bad_weather_1 1 15.7 95059 34195
## - grass_1 1 16.2 95060 34195
## - home_team_1 1 16.4 95060 34195
## - weight 1 26.1 95069 34198
## - NYJ 1 30.7 95074 34199
## - DEN 1 31.4 95075 34199
## - CAR 1 32.1 95075 34199
## - NE 1 37.6 95081 34201
## - TB 1 37.8 95081 34201
## - BUF 1 45.2 95089 34203
## - DAL 1 48.0 95091 34204
## - cold_weather 1 48.3 95092 34204
## - TEN 1 58.1 95102 34207
## - ARI 1 73.6 95117 34211
## - NYG 1 75.0 95118 34212
## - STL 1 87.9 95131 34216
## - MIA 1 88.6 95132 34216
## - JAC 1 91.1 95135 34217
## - PHI 1 91.3 95135 34217
## - SD 1 95.4 95139 34218
## - NOR 1 96.7 95140 34218
## - IND 1 97.7 95141 34218
## - OAK 1 100.6 95144 34219
## - WAS 1 101.9 95145 34220
## - KC 1 104.0 95147 34220
## - CIN 1 108.3 95152 34222
## - height 1 114.7 95158 34223
## - CHI 1 119.5 95163 34225
## - HOU 1 130.9 95174 34228
## - ATL 1 133.2 95177 34229
## - BAL 1 135.2 95179 34229
## - MINN 1 138.5 95182 34230
## - DET 1 138.6 95182 34230
## - PIT 1 141.2 95185 34231
## - CLE 1 191.2 95235 34245
## - avg_rbry_pos 1 261.3 95305 34266
## - avg_qbtdp_plyr 1 551.8 95595 34349
## - avg_rbry_plyr 1 1044.5 96088 34491
## - avg_rectd_plyr 1 25930.1 120973 40820
##
## Step: AIC=34190.87
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_fuml_plyr 1 3.2 95049 34190
## - hot_weather 1 5.6 95051 34190
## - GB 1 5.8 95052 34191
## - vertical1 1 5.9 95052 34191
## - forty1 1 6.8 95052 34191
## <none> 95046 34191
## - bad_weather_1 1 15.7 95061 34193
## - home_team_1 1 16.2 95062 34194
## - grass_1 1 18.2 95064 34194
## - weight 1 26.1 95072 34196
## - NYJ 1 30.7 95076 34198
## - DEN 1 31.3 95077 34198
## - CAR 1 31.9 95078 34198
## - TB 1 38.4 95084 34200
## - NE 1 39.0 95085 34200
## - cold_weather 1 47.0 95093 34202
## - BUF 1 47.7 95093 34203
## - DAL 1 50.7 95096 34204
## - TEN 1 62.3 95108 34207
## - ARI 1 81.5 95127 34212
## - NYG 1 84.1 95130 34213
## - STL 1 98.5 95144 34217
## - MIA 1 98.7 95144 34217
## - JAC 1 101.3 95147 34218
## - PHI 1 101.8 95147 34218
## - SD 1 106.3 95152 34220
## - IND 1 111.6 95157 34221
## - NOR 1 111.8 95157 34221
## - OAK 1 113.8 95159 34222
## - height 1 114.9 95161 34222
## - WAS 1 115.7 95161 34222
## - KC 1 118.1 95164 34223
## - CIN 1 125.0 95171 34225
## - CHI 1 135.8 95182 34228
## - HOU 1 152.2 95198 34233
## - ATL 1 154.9 95201 34234
## - BAL 1 159.7 95205 34235
## - DET 1 160.9 95207 34235
## - MINN 1 161.4 95207 34236
## - PIT 1 165.0 95211 34237
## - CLE 1 225.4 95271 34254
## - avg_rbry_pos 1 261.6 95307 34264
## - avg_qbtdp_plyr 1 550.2 95596 34347
## - avg_rbry_plyr 1 1045.6 96091 34490
## - avg_rectd_plyr 1 25931.2 120977 40819
##
## Step: AIC=34189.79
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 5.6 95054 34189
## - vertical1 1 5.8 95055 34189
## - GB 1 5.9 95055 34190
## - forty1 1 6.9 95056 34190
## <none> 95049 34190
## - bad_weather_1 1 15.6 95064 34192
## - home_team_1 1 16.3 95065 34193
## - grass_1 1 18.1 95067 34193
## - weight 1 24.7 95074 34195
## - NYJ 1 29.8 95079 34196
## - DEN 1 30.6 95079 34197
## - CAR 1 31.4 95080 34197
## - TB 1 37.6 95086 34199
## - NE 1 40.0 95089 34199
## - cold_weather 1 46.7 95096 34201
## - BUF 1 46.9 95096 34201
## - DAL 1 50.4 95099 34202
## - TEN 1 61.2 95110 34205
## - ARI 1 80.4 95129 34211
## - NYG 1 83.3 95132 34212
## - STL 1 97.3 95146 34216
## - MIA 1 97.6 95147 34216
## - PHI 1 100.0 95149 34217
## - JAC 1 100.8 95150 34217
## - SD 1 105.5 95154 34218
## - IND 1 110.9 95160 34220
## - NOR 1 112.2 95161 34220
## - OAK 1 113.6 95162 34221
## - WAS 1 114.1 95163 34221
## - height 1 117.2 95166 34222
## - KC 1 117.3 95166 34222
## - CIN 1 124.3 95173 34224
## - CHI 1 134.1 95183 34227
## - HOU 1 152.1 95201 34232
## - ATL 1 155.7 95205 34233
## - DET 1 159.4 95208 34234
## - BAL 1 159.5 95208 34234
## - MINN 1 160.6 95209 34234
## - PIT 1 163.5 95212 34235
## - CLE 1 223.1 95272 34252
## - avg_rbry_pos 1 262.8 95312 34264
## - avg_qbtdp_plyr 1 913.6 95962 34451
## - avg_rbry_plyr 1 1132.3 96181 34513
## - avg_rectd_plyr 1 25934.9 120984 40819
##
## Step: AIC=34189.41
## rec ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 5.8 95060 34189
## - GB 1 6.2 95061 34189
## <none> 95054 34189
## - forty1 1 6.9 95061 34189
## - bad_weather_1 1 15.4 95070 34192
## - home_team_1 1 16.2 95071 34192
## - grass_1 1 19.6 95074 34193
## - weight 1 24.4 95079 34194
## - NYJ 1 29.4 95084 34196
## - DEN 1 31.0 95085 34196
## - CAR 1 32.2 95087 34197
## - TB 1 37.3 95092 34198
## - NE 1 40.5 95095 34199
## - cold_weather 1 45.7 95100 34201
## - BUF 1 46.5 95101 34201
## - DAL 1 51.1 95106 34202
## - TEN 1 62.3 95117 34205
## - ARI 1 81.3 95136 34211
## - NYG 1 84.0 95138 34212
## - STL 1 96.8 95151 34215
## - MIA 1 99.0 95153 34216
## - PHI 1 101.3 95156 34217
## - JAC 1 102.3 95157 34217
## - SD 1 104.5 95159 34218
## - IND 1 111.8 95166 34220
## - NOR 1 112.2 95167 34220
## - OAK 1 115.3 95170 34221
## - WAS 1 115.6 95170 34221
## - height 1 117.5 95172 34221
## - KC 1 118.9 95173 34222
## - CIN 1 125.3 95180 34224
## - CHI 1 135.6 95190 34227
## - HOU 1 153.4 95208 34232
## - ATL 1 157.0 95212 34233
## - DET 1 160.7 95215 34234
## - BAL 1 160.7 95215 34234
## - MINN 1 161.8 95216 34234
## - PIT 1 163.9 95218 34235
## - CLE 1 225.1 95280 34252
## - avg_rbry_pos 1 262.5 95317 34263
## - avg_qbtdp_plyr 1 913.0 95967 34450
## - avg_rbry_plyr 1 1131.0 96185 34513
## - avg_rectd_plyr 1 25935.9 120990 40818
##
## Step: AIC=34189.08
## rec ~ height + weight + cold_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR +
## NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - forty1 1 2.6 95063 34188
## - GB 1 6.7 95067 34189
## <none> 95060 34189
## - bad_weather_1 1 15.5 95076 34192
## - home_team_1 1 16.2 95076 34192
## - grass_1 1 19.5 95080 34193
## - weight 1 26.3 95086 34195
## - NYJ 1 28.5 95089 34195
## - DEN 1 30.3 95091 34196
## - CAR 1 32.2 95092 34196
## - TB 1 38.1 95098 34198
## - NE 1 41.1 95101 34199
## - cold_weather 1 45.8 95106 34200
## - BUF 1 48.2 95108 34201
## - DAL 1 51.6 95112 34202
## - TEN 1 62.1 95122 34205
## - ARI 1 82.8 95143 34211
## - NYG 1 84.8 95145 34212
## - STL 1 98.8 95159 34216
## - JAC 1 100.2 95160 34216
## - MIA 1 100.9 95161 34216
## - PHI 1 103.1 95163 34217
## - SD 1 105.6 95166 34218
## - IND 1 111.2 95171 34219
## - NOR 1 112.6 95173 34220
## - WAS 1 116.2 95176 34221
## - OAK 1 117.6 95178 34221
## - height 1 118.8 95179 34221
## - KC 1 119.6 95180 34222
## - CIN 1 126.4 95187 34224
## - CHI 1 138.1 95198 34227
## - HOU 1 152.5 95213 34231
## - DET 1 159.2 95219 34233
## - MINN 1 160.4 95221 34233
## - ATL 1 160.7 95221 34234
## - BAL 1 161.7 95222 34234
## - PIT 1 164.8 95225 34235
## - CLE 1 223.7 95284 34252
## - avg_rbry_pos 1 261.0 95321 34262
## - avg_qbtdp_plyr 1 909.6 95970 34449
## - avg_rbry_plyr 1 1145.3 96206 34516
## - avg_rectd_plyr 1 25958.6 121019 40823
##
## Step: AIC=34187.84
## rec ~ height + weight + cold_weather + home_team_1 + ARI + ATL +
## BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB +
## HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - GB 1 6.4 95069 34188
## <none> 95063 34188
## - bad_weather_1 1 15.5 95078 34190
## - home_team_1 1 16.2 95079 34191
## - grass_1 1 19.5 95082 34191
## - NYJ 1 28.2 95091 34194
## - DEN 1 30.0 95093 34195
## - CAR 1 32.6 95096 34195
## - TB 1 37.8 95101 34197
## - NE 1 39.1 95102 34197
## - weight 1 41.6 95104 34198
## - cold_weather 1 45.8 95109 34199
## - BUF 1 48.4 95111 34200
## - DAL 1 51.1 95114 34201
## - TEN 1 61.8 95125 34204
## - ARI 1 83.3 95146 34210
## - NYG 1 83.6 95147 34210
## - STL 1 97.4 95160 34214
## - JAC 1 99.8 95163 34215
## - MIA 1 100.1 95163 34215
## - PHI 1 102.5 95165 34215
## - SD 1 104.1 95167 34216
## - IND 1 111.5 95174 34218
## - NOR 1 112.5 95175 34218
## - WAS 1 117.4 95180 34220
## - height 1 118.3 95181 34220
## - OAK 1 118.8 95182 34220
## - KC 1 119.3 95182 34220
## - CIN 1 125.1 95188 34222
## - CHI 1 137.7 95201 34226
## - HOU 1 151.0 95214 34229
## - DET 1 158.5 95221 34232
## - ATL 1 159.0 95222 34232
## - MINN 1 160.1 95223 34232
## - BAL 1 161.3 95224 34232
## - PIT 1 164.1 95227 34233
## - CLE 1 222.9 95286 34250
## - avg_rbry_pos 1 260.4 95323 34261
## - avg_qbtdp_plyr 1 1172.9 96236 34523
## - avg_rbry_plyr 1 1198.2 96261 34530
## - avg_rectd_plyr 1 26926.6 121990 41040
##
## Step: AIC=34187.7
## rec ~ height + weight + cold_weather + home_team_1 + ARI + ATL +
## BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU +
## IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## <none> 95069 34188
## - bad_weather_1 1 15.3 95085 34190
## - home_team_1 1 16.5 95086 34190
## - grass_1 1 17.8 95087 34191
## - NYJ 1 22.5 95092 34192
## - DEN 1 24.1 95093 34193
## - CAR 1 26.7 95096 34193
## - TB 1 31.7 95101 34195
## - NE 1 32.8 95102 34195
## - weight 1 41.2 95110 34198
## - BUF 1 42.1 95111 34198
## - cold_weather 1 44.0 95113 34198
## - DAL 1 44.7 95114 34199
## - TEN 1 55.3 95125 34202
## - ARI 1 77.0 95146 34208
## - NYG 1 77.5 95147 34208
## - STL 1 91.3 95161 34212
## - JAC 1 93.9 95163 34213
## - MIA 1 94.3 95164 34213
## - PHI 1 96.7 95166 34214
## - SD 1 98.4 95168 34214
## - IND 1 105.9 95175 34216
## - NOR 1 107.4 95177 34217
## - WAS 1 112.3 95182 34218
## - OAK 1 113.8 95183 34219
## - KC 1 114.3 95184 34219
## - height 1 118.4 95188 34220
## - CIN 1 119.9 95189 34220
## - CHI 1 133.1 95202 34224
## - HOU 1 146.7 95216 34228
## - DET 1 154.5 95224 34230
## - ATL 1 155.2 95224 34231
## - MINN 1 156.0 95225 34231
## - BAL 1 158.2 95227 34231
## - PIT 1 161.6 95231 34232
## - CLE 1 222.9 95292 34250
## - avg_rbry_pos 1 257.9 95327 34260
## - avg_qbtdp_plyr 1 1167.3 96237 34521
## - avg_rbry_plyr 1 1195.7 96265 34529
## - avg_rectd_plyr 1 27169.4 122239 41094AIC appeared to be very similar to the linear regression
Targets
Preprocess:
set.seed(123)
splittrg <- sample.split(nfl_data$trg, SplitRatio = 0.7)
Traintrg <- subset(nfl_data, split == TRUE)
Testtrg <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Traintrg, method = c("center", "scale"))
trainTransformedtrg <- predict(preProcValues, Traintrg)
testTransformedtrg <- predict(preProcValues, Testtrg)ggpairs:
ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[46:51]))])
trgregform <- formula(paste("trg ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegtrg <- lm(trgregform, data = trainTransformedtrg)
summary(linRegtrg)##
## Call:
## lm(formula = trgregform, data = trainTransformedtrg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7736 -0.4601 -0.1111 0.3197 5.3233
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.716e-15 4.567e-03 0.000 1.000000
## height -1.979e-02 8.861e-03 -2.234 0.025511 *
## weight -6.511e-02 8.305e-03 -7.840 4.68e-15 ***
## cold_weather -7.148e-03 4.808e-03 -1.487 0.137097
## hot_weather -5.357e-03 4.609e-03 -1.162 0.245100
## home_team_1 -1.690e-02 4.969e-03 -3.402 0.000671 ***
## forty1 -4.129e-02 7.882e-03 -5.238 1.63e-07 ***
## vertical1 6.284e-04 6.060e-03 0.104 0.917408
## ARI 3.596e-02 6.389e-03 5.629 1.83e-08 ***
## ATL 2.773e-02 6.419e-03 4.320 1.57e-05 ***
## BAL 3.933e-02 6.425e-03 6.121 9.43e-10 ***
## BUF 2.473e-02 6.342e-03 3.899 9.67e-05 ***
## CAR 2.227e-02 6.301e-03 3.535 0.000409 ***
## CHI 2.860e-02 6.231e-03 4.591 4.43e-06 ***
## CIN 2.927e-02 6.345e-03 4.612 4.00e-06 ***
## CLE 5.271e-02 6.316e-03 8.345 < 2e-16 ***
## DAL 7.146e-03 6.380e-03 1.120 0.262697
## DEN 1.239e-02 6.404e-03 1.935 0.053034 .
## DET 3.610e-02 6.316e-03 5.715 1.11e-08 ***
## GB -7.034e-03 6.503e-03 -1.082 0.279411
## HOU 4.004e-02 6.425e-03 6.231 4.69e-10 ***
## IND 3.530e-02 6.378e-03 5.535 3.14e-08 ***
## JAC 3.907e-02 6.222e-03 6.280 3.45e-10 ***
## KC 2.922e-02 6.358e-03 4.595 4.34e-06 ***
## MIA 2.997e-02 6.256e-03 4.790 1.68e-06 ***
## MINN 3.504e-02 6.294e-03 5.568 2.61e-08 ***
## NE 1.349e-02 6.573e-03 2.052 0.040222 *
## NOR 1.142e-02 6.553e-03 1.742 0.081465 .
## NYG 2.910e-02 6.405e-03 4.543 5.58e-06 ***
## NYJ 2.792e-02 6.382e-03 4.374 1.22e-05 ***
## OAK 3.254e-02 6.422e-03 5.067 4.07e-07 ***
## PHI 3.026e-02 6.223e-03 4.863 1.16e-06 ***
## PIT 2.865e-02 6.386e-03 4.486 7.29e-06 ***
## SD 2.118e-02 6.267e-03 3.380 0.000726 ***
## SEA -1.205e-02 6.504e-03 -1.852 0.064026 .
## STL 3.460e-02 6.330e-03 5.467 4.63e-08 ***
## TB 2.346e-02 6.271e-03 3.741 0.000184 ***
## TEN 2.529e-02 6.309e-03 4.009 6.10e-05 ***
## WAS 2.534e-02 6.342e-03 3.995 6.48e-05 ***
## avg_trg_team NA NA NA NA
## avg_rectd_plyr 5.746e-01 5.832e-03 98.521 < 2e-16 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr 1.037e-01 6.980e-03 14.855 < 2e-16 ***
## avg_rbry_pos -1.073e-01 8.133e-03 -13.197 < 2e-16 ***
## avg_fuml_plyr -2.183e-02 6.747e-03 -3.235 0.001216 **
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -8.681e-02 7.328e-03 -11.846 < 2e-16 ***
## avg_qbtdp_team NA NA NA NA
## grass_1 -7.245e-03 5.255e-03 -1.379 0.168009
## bad_weather_1 -6.780e-04 4.646e-03 -0.146 0.883979
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7572 on 27438 degrees of freedom
## Multiple R-squared: 0.4276, Adjusted R-squared: 0.4267
## F-statistic: 455.5 on 45 and 27438 DF, p-value: < 2.2e-16linRegtrg2 <- update(linRegtrg, ~. -height-cold_weather-hot_weather-forty1-vertical1-DAL-DEN-GB-NE-NOR-SEA
-avg_trg_team -avg_tdr_team-avg_rbra_team -avg_fuml_team -avg_qbtdp_team
-avg_qbints_team - grass_1-bad_weather_1)
summary(linRegtrg2)##
## Call:
## lm(formula = trg ~ weight + home_team_1 + ARI + ATL + BAL + BUF +
## CAR + CHI + CIN + CLE + DET + HOU + IND + JAC + KC + MIA +
## MINN + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr, data = trainTransformedtrg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8593 -0.4634 -0.1128 0.3281 5.3615
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.617e-15 4.573e-03 0.000 1.000000
## weight -1.000e-01 4.631e-03 -21.594 < 2e-16 ***
## home_team_1 -1.995e-02 4.823e-03 -4.137 3.53e-05 ***
## ARI 3.395e-02 4.851e-03 6.998 2.65e-12 ***
## ATL 2.430e-02 4.838e-03 5.023 5.12e-07 ***
## BAL 3.640e-02 4.823e-03 7.547 4.60e-14 ***
## BUF 2.220e-02 4.806e-03 4.620 3.85e-06 ***
## CAR 2.035e-02 4.811e-03 4.230 2.35e-05 ***
## CHI 2.459e-02 4.801e-03 5.121 3.07e-07 ***
## CIN 2.530e-02 4.804e-03 5.267 1.40e-07 ***
## CLE 4.859e-02 4.839e-03 10.040 < 2e-16 ***
## DET 3.359e-02 4.811e-03 6.982 2.97e-12 ***
## HOU 3.599e-02 4.859e-03 7.407 1.33e-13 ***
## IND 3.378e-02 4.822e-03 7.006 2.51e-12 ***
## JAC 3.626e-02 4.795e-03 7.560 4.14e-14 ***
## KC 2.514e-02 4.825e-03 5.211 1.89e-07 ***
## MIA 2.625e-02 4.798e-03 5.471 4.51e-08 ***
## MINN 3.226e-02 4.816e-03 6.699 2.14e-11 ***
## NYG 2.505e-02 4.808e-03 5.209 1.91e-07 ***
## NYJ 2.517e-02 4.822e-03 5.219 1.81e-07 ***
## OAK 2.971e-02 4.823e-03 6.160 7.39e-10 ***
## PHI 2.672e-02 4.802e-03 5.564 2.66e-08 ***
## PIT 2.404e-02 4.811e-03 4.997 5.85e-07 ***
## SD 1.560e-02 4.791e-03 3.257 0.001128 **
## STL 3.048e-02 4.848e-03 6.288 3.27e-10 ***
## TB 2.000e-02 4.806e-03 4.161 3.17e-05 ***
## TEN 2.184e-02 4.823e-03 4.527 6.00e-06 ***
## WAS 2.395e-02 4.822e-03 4.966 6.87e-07 ***
## avg_rectd_plyr 5.810e-01 5.664e-03 102.579 < 2e-16 ***
## avg_rbry_plyr 1.091e-01 6.871e-03 15.871 < 2e-16 ***
## avg_rbry_pos -9.647e-02 7.087e-03 -13.613 < 2e-16 ***
## avg_fuml_plyr -2.280e-02 6.723e-03 -3.391 0.000696 ***
## avg_qbtdp_plyr -1.057e-01 6.619e-03 -15.977 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.758 on 27451 degrees of freedom
## Multiple R-squared: 0.426, Adjusted R-squared: 0.4254
## F-statistic: 636.7 on 32 and 27451 DF, p-value: < 2.2e-16Modest gains in second run’s R2. It is a much more simple model, and has a little better descriptive stats.
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
TrgPredicted <- predict(linRegtrg2, newdata = testTransformedtrg)
SSEtrg <- sum((TrgPredicted - testTransformedtrg$trg)^2)
SSTtrg <- sum((mean(nfl_data$trg)-testTransformedtrg$trg)^2)
r2_trg <- 1 - SSEtrg/SSTtrg
r2_trg## [1] 0.953245rmse_trg <- sqrt(SSEtrg/nrow(testTransformedtrg))
rmse_trg## [1] 0.7421937The regression plots for targets are below:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegrec2, which = c(1:3,5))
Here are additional summary statistics:
confint(linRegtrg2)## 2.5 % 97.5 %
## (Intercept) -0.008962372 0.008962372
## weight -0.109072460 -0.090919689
## home_team_1 -0.029407521 -0.010499863
## ARI 0.024443139 0.043461176
## ATL 0.014816272 0.033779985
## BAL 0.026945513 0.045852511
## BUF 0.012784765 0.031622921
## CAR 0.010919267 0.029777561
## CHI 0.015174471 0.033995707
## CIN 0.015884937 0.034717487
## CLE 0.039102914 0.058073333
## DET 0.024163320 0.043024446
## HOU 0.026466108 0.045512540
## IND 0.024332465 0.043237109
## JAC 0.026856263 0.045654833
## KC 0.015685651 0.034600137
## MIA 0.016847793 0.035657765
## MINN 0.022823096 0.041702343
## NYG 0.015622503 0.034469521
## NYJ 0.015717405 0.034621023
## OAK 0.020253373 0.039158780
## PHI 0.017304578 0.036128312
## PIT 0.014610681 0.033468501
## SD 0.006212349 0.024992919
## STL 0.020979488 0.039984055
## TB 0.010580046 0.029420028
## TEN 0.012383540 0.031291995
## WAS 0.014495624 0.033398144
## avg_rectd_plyr 0.569942774 0.592147559
## avg_rbry_plyr 0.095582869 0.122518021
## avg_rbry_pos -0.110362600 -0.082581821
## avg_fuml_plyr -0.035976124 -0.009622626
## avg_qbtdp_plyr -0.118718776 -0.092772666coef(summary(linRegtrg2))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.616974e-15 0.004572521 -3.536285e-13 1.000000e+00
## weight -9.999607e-02 0.004630690 -2.159421e+01 1.455031e-102
## home_team_1 -1.995369e-02 0.004823258 -4.136974e+00 3.529640e-05
## ARI 3.395216e-02 0.004851415 6.998403e+00 2.648420e-12
## ATL 2.429813e-02 0.004837557 5.022809e+00 5.124010e-07
## BAL 3.639901e-02 0.004823090 7.546825e+00 4.598244e-14
## BUF 2.220384e-02 0.004805528 4.620479e+00 3.845937e-06
## CAR 2.034841e-02 0.004810665 4.229854e+00 2.346000e-05
## CHI 2.458509e-02 0.004801212 5.120601e+00 3.066202e-07
## CIN 2.530121e-02 0.004804098 5.266589e+00 1.400281e-07
## CLE 4.858812e-02 0.004839268 1.004039e+01 1.112750e-23
## DET 3.359388e-02 0.004811388 6.982160e+00 2.972888e-12
## HOU 3.598932e-02 0.004858659 7.407255e+00 1.326510e-13
## IND 3.378479e-02 0.004822489 7.005674e+00 2.514675e-12
## JAC 3.625555e-02 0.004795430 7.560437e+00 4.142604e-14
## KC 2.514289e-02 0.004825000 5.210963e+00 1.892202e-07
## MIA 2.625278e-02 0.004798339 5.471222e+00 4.508438e-08
## MINN 3.226272e-02 0.004816010 6.699055e+00 2.138233e-11
## NYG 2.504601e-02 0.004807789 5.209465e+00 1.907521e-07
## NYJ 2.516921e-02 0.004822228 5.219416e+00 1.807925e-07
## OAK 2.970608e-02 0.004822684 6.159657e+00 7.391443e-10
## PHI 2.671644e-02 0.004801849 5.563782e+00 2.664494e-08
## PIT 2.403959e-02 0.004810545 4.997270e+00 5.850484e-07
## SD 1.560263e-02 0.004790839 3.256765e+00 1.128265e-03
## STL 3.048177e-02 0.004847979 6.287521e+00 3.274283e-10
## TB 2.000004e-02 0.004805994 4.161478e+00 3.171574e-05
## TEN 2.183777e-02 0.004823461 4.527406e+00 5.996295e-06
## WAS 2.394688e-02 0.004821948 4.966227e+00 6.867755e-07
## avg_rectd_plyr 5.810452e-01 0.005664340 1.025795e+02 0.000000e+00
## avg_rbry_plyr 1.090504e-01 0.006871035 1.587104e+01 1.794185e-56
## avg_rbry_pos -9.647221e-02 0.007086751 -1.361304e+01 4.589358e-42
## avg_fuml_plyr -2.279937e-02 0.006722658 -3.391423e+00 6.962880e-04
## avg_qbtdp_plyr -1.057457e-01 0.006618735 -1.597673e+01 3.363564e-57anova(linRegtrg2)## Analysis of Variance Table
##
## Response: trg
## Df Sum Sq Mean Sq F value Pr(>F)
## weight 1 359.6 359.6 625.8500 < 2.2e-16 ***
## home_team_1 1 18.1 18.1 31.4392 2.078e-08 ***
## ARI 1 0.2 0.2 0.3197 0.571799
## ATL 1 6.1 6.1 10.6206 0.001120 **
## BAL 1 0.9 0.9 1.6206 0.203025
## BUF 1 0.8 0.8 1.3448 0.246194
## CAR 1 0.6 0.6 1.0163 0.313413
## CHI 1 0.0 0.0 0.0073 0.932089
## CIN 1 0.3 0.3 0.5180 0.471689
## CLE 1 0.0 0.0 0.0621 0.803255
## DET 1 21.4 21.4 37.2209 1.069e-09 ***
## HOU 1 1.1 1.1 1.8455 0.174323
## IND 1 11.6 11.6 20.1547 7.171e-06 ***
## JAC 1 2.0 2.0 3.4702 0.062494 .
## KC 1 6.0 6.0 10.4925 0.001200 **
## MIA 1 0.7 0.7 1.2103 0.271286
## MINN 1 1.0 1.0 1.7083 0.191223
## NYG 1 3.7 3.7 6.3533 0.011722 *
## NYJ 1 0.6 0.6 1.1157 0.290857
## OAK 1 1.0 1.0 1.7412 0.186993
## PHI 1 3.8 3.8 6.6112 0.010139 *
## PIT 1 5.0 5.0 8.7286 0.003135 **
## SD 1 1.0 1.0 1.7287 0.188586
## STL 1 3.0 3.0 5.1518 0.023230 *
## TB 1 0.5 0.5 0.7916 0.373618
## TEN 1 3.7 3.7 6.4768 0.010935 *
## WAS 1 0.6 0.6 1.0442 0.306864
## avg_rectd_plyr 1 10771.0 10771.0 18744.1659 < 2.2e-16 ***
## avg_rbry_plyr 1 74.1 74.1 128.9315 < 2.2e-16 ***
## avg_rbry_pos 1 58.0 58.0 101.0080 < 2.2e-16 ***
## avg_fuml_plyr 1 205.7 205.7 357.9520 < 2.2e-16 ***
## avg_qbtdp_plyr 1 146.7 146.7 255.2558 < 2.2e-16 ***
## Residuals 27451 15774.3 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1This one was an improvement over the previous models. It still has its problems, and may need some refinement or other variables to improve the predictions.
AIC:
aic_trg <- step(lm(trgregform, data = trainTransformedtrg), direction = "backward")## Start: AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 0.0 15730 -15246.2
## - bad_weather_1 1 0.0 15730 -15246.2
## - GB 1 0.7 15731 -15245.0
## - DAL 1 0.7 15731 -15244.9
## - hot_weather 1 0.8 15731 -15244.9
## - grass_1 1 1.1 15732 -15244.3
## <none> 15730 -15244.2
## - cold_weather 1 1.3 15732 -15244.0
## - NOR 1 1.7 15732 -15243.2
## - SEA 1 2.0 15732 -15242.8
## - DEN 1 2.1 15733 -15242.5
## - NE 1 2.4 15733 -15242.0
## - height 1 2.9 15733 -15241.2
## - avg_fuml_plyr 1 6.0 15736 -15235.7
## - SD 1 6.5 15737 -15234.8
## - home_team_1 1 6.6 15737 -15234.6
## - CAR 1 7.2 15738 -15233.7
## - TB 1 8.0 15738 -15232.2
## - BUF 1 8.7 15739 -15231.0
## - WAS 1 9.2 15740 -15230.2
## - TEN 1 9.2 15740 -15230.1
## - ATL 1 10.7 15741 -15227.5
## - NYJ 1 11.0 15741 -15227.0
## - PIT 1 11.5 15742 -15226.1
## - NYG 1 11.8 15742 -15225.5
## - CHI 1 12.1 15742 -15225.1
## - KC 1 12.1 15743 -15225.1
## - CIN 1 12.2 15743 -15224.9
## - MIA 1 13.2 15744 -15223.2
## - PHI 1 13.6 15744 -15222.5
## - OAK 1 14.7 15745 -15220.5
## - forty1 1 15.7 15746 -15218.7
## - STL 1 17.1 15748 -15216.3
## - IND 1 17.6 15748 -15215.5
## - MINN 1 17.8 15748 -15215.2
## - ARI 1 18.2 15749 -15214.5
## - DET 1 18.7 15749 -15213.5
## - BAL 1 21.5 15752 -15208.7
## - HOU 1 22.3 15753 -15207.3
## - JAC 1 22.6 15753 -15206.7
## - weight 1 35.2 15766 -15184.7
## - CLE 1 39.9 15770 -15176.5
## - avg_qbtdp_plyr 1 80.5 15811 -15106.0
## - avg_rbry_pos 1 99.9 15830 -15072.3
## - avg_rbry_plyr 1 126.5 15857 -15026.1
## - avg_rectd_plyr 1 5564.7 21295 -6921.8
##
## Step: AIC=-15246.19
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - bad_weather_1 1 0.0 15730 -15248.2
## - GB 1 0.7 15731 -15247.0
## - DAL 1 0.7 15731 -15246.9
## - hot_weather 1 0.8 15731 -15246.8
## - grass_1 1 1.1 15732 -15246.3
## <none> 15730 -15246.2
## - cold_weather 1 1.3 15732 -15246.0
## - NOR 1 1.7 15732 -15245.2
## - SEA 1 2.0 15732 -15244.8
## - DEN 1 2.2 15733 -15244.4
## - NE 1 2.4 15733 -15244.0
## - height 1 2.9 15733 -15243.2
## - avg_fuml_plyr 1 6.0 15736 -15237.7
## - SD 1 6.5 15737 -15236.8
## - home_team_1 1 6.6 15737 -15236.6
## - CAR 1 7.2 15738 -15235.7
## - TB 1 8.0 15738 -15234.2
## - BUF 1 8.7 15739 -15233.0
## - WAS 1 9.1 15740 -15232.2
## - TEN 1 9.2 15740 -15232.1
## - ATL 1 10.7 15741 -15229.5
## - NYJ 1 11.0 15742 -15229.0
## - PIT 1 11.5 15742 -15228.1
## - NYG 1 11.8 15742 -15227.5
## - CHI 1 12.1 15743 -15227.1
## - KC 1 12.1 15743 -15227.1
## - CIN 1 12.2 15743 -15226.9
## - MIA 1 13.2 15744 -15225.2
## - PHI 1 13.6 15744 -15224.5
## - OAK 1 14.7 15745 -15222.5
## - STL 1 17.1 15748 -15218.3
## - IND 1 17.6 15748 -15217.5
## - MINN 1 17.8 15748 -15217.1
## - ARI 1 18.2 15749 -15216.5
## - DET 1 18.7 15749 -15215.5
## - BAL 1 21.5 15752 -15210.7
## - forty1 1 22.0 15752 -15209.8
## - HOU 1 22.3 15753 -15209.3
## - JAC 1 22.7 15753 -15208.6
## - weight 1 35.3 15766 -15186.5
## - CLE 1 40.0 15770 -15178.5
## - avg_qbtdp_plyr 1 80.5 15811 -15107.9
## - avg_rbry_pos 1 99.9 15830 -15074.2
## - avg_rbry_plyr 1 126.8 15857 -15027.6
## - avg_rectd_plyr 1 5578.3 21309 -6906.2
##
## Step: AIC=-15248.17
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - GB 1 0.7 15731 -15249.0
## - DAL 1 0.7 15731 -15248.9
## - hot_weather 1 0.8 15731 -15248.8
## - grass_1 1 1.1 15732 -15248.3
## <none> 15730 -15248.2
## - cold_weather 1 1.3 15732 -15247.9
## - NOR 1 1.7 15732 -15247.1
## - SEA 1 2.0 15732 -15246.7
## - DEN 1 2.2 15733 -15246.4
## - NE 1 2.4 15733 -15246.0
## - height 1 2.9 15733 -15245.2
## - avg_fuml_plyr 1 6.0 15736 -15239.7
## - SD 1 6.6 15737 -15238.7
## - home_team_1 1 6.7 15737 -15238.6
## - CAR 1 7.2 15738 -15237.7
## - TB 1 8.0 15738 -15236.1
## - BUF 1 8.7 15739 -15235.0
## - WAS 1 9.1 15740 -15234.2
## - TEN 1 9.2 15740 -15234.0
## - ATL 1 10.7 15741 -15231.5
## - NYJ 1 11.0 15742 -15231.0
## - PIT 1 11.5 15742 -15230.0
## - NYG 1 11.8 15742 -15229.5
## - CHI 1 12.1 15743 -15229.1
## - KC 1 12.1 15743 -15229.0
## - CIN 1 12.2 15743 -15228.9
## - MIA 1 13.2 15744 -15227.2
## - PHI 1 13.6 15744 -15226.5
## - OAK 1 14.7 15745 -15224.5
## - STL 1 17.2 15748 -15220.2
## - IND 1 17.6 15748 -15219.5
## - MINN 1 17.8 15748 -15219.1
## - ARI 1 18.2 15749 -15218.4
## - DET 1 18.7 15749 -15217.4
## - BAL 1 21.5 15752 -15212.6
## - forty1 1 22.0 15752 -15211.8
## - HOU 1 22.3 15753 -15211.3
## - JAC 1 22.7 15753 -15210.5
## - weight 1 35.3 15766 -15188.5
## - CLE 1 39.9 15770 -15180.5
## - avg_qbtdp_plyr 1 80.5 15811 -15109.9
## - avg_rbry_pos 1 99.9 15830 -15076.1
## - avg_rbry_plyr 1 126.8 15857 -15029.6
## - avg_rectd_plyr 1 5578.7 21309 -6907.7
##
## Step: AIC=-15248.99
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.8 15732 -15249.6
## - grass_1 1 1.1 15732 -15249.1
## <none> 15731 -15249.0
## - SEA 1 1.3 15732 -15248.7
## - cold_weather 1 1.5 15733 -15248.4
## - DAL 1 2.1 15733 -15247.3
## - height 1 2.8 15734 -15246.0
## - NOR 1 4.1 15735 -15243.8
## - DEN 1 4.8 15736 -15242.5
## - NE 1 5.3 15736 -15241.7
## - avg_fuml_plyr 1 5.9 15737 -15240.6
## - home_team_1 1 6.6 15738 -15239.4
## - SD 1 11.7 15743 -15230.6
## - CAR 1 12.7 15744 -15228.8
## - TB 1 13.9 15745 -15226.8
## - BUF 1 14.9 15746 -15225.0
## - WAS 1 15.8 15747 -15223.4
## - TEN 1 15.8 15747 -15223.4
## - ATL 1 18.0 15749 -15219.6
## - NYJ 1 18.5 15750 -15218.7
## - PIT 1 19.7 15751 -15216.6
## - CHI 1 19.8 15751 -15216.3
## - NYG 1 19.9 15751 -15216.2
## - CIN 1 20.2 15751 -15215.7
## - KC 1 20.3 15752 -15215.6
## - MIA 1 21.6 15753 -15213.3
## - PHI 1 22.1 15753 -15212.4
## - forty1 1 22.2 15753 -15212.3
## - OAK 1 24.2 15755 -15208.8
## - STL 1 27.0 15758 -15203.9
## - MINN 1 28.0 15759 -15202.1
## - IND 1 28.1 15759 -15201.9
## - ARI 1 28.7 15760 -15200.9
## - DET 1 29.5 15761 -15199.5
## - BAL 1 34.5 15766 -15190.8
## - HOU 1 34.7 15766 -15190.3
## - JAC 1 35.1 15766 -15189.6
## - weight 1 35.3 15766 -15189.4
## - CLE 1 60.1 15791 -15146.1
## - avg_qbtdp_plyr 1 81.2 15812 -15109.4
## - avg_rbry_pos 1 100.4 15832 -15076.1
## - avg_rbry_plyr 1 126.7 15858 -15030.4
## - avg_rectd_plyr 1 5600.2 21331 -6881.1
##
## Step: AIC=-15249.63
## trg ~ height + weight + cold_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## <none> 15732 -15249.6
## - grass_1 1 1.3 15733 -15249.4
## - cold_weather 1 1.4 15733 -15249.1
## - SEA 1 1.4 15733 -15249.1
## - DAL 1 2.1 15734 -15248.0
## - height 1 2.9 15735 -15246.6
## - NOR 1 4.0 15736 -15244.6
## - DEN 1 4.8 15737 -15243.3
## - NE 1 5.2 15737 -15242.5
## - avg_fuml_plyr 1 5.9 15738 -15241.3
## - home_team_1 1 6.6 15738 -15240.1
## - SD 1 11.4 15743 -15231.7
## - CAR 1 12.7 15745 -15229.4
## - TB 1 13.7 15746 -15227.8
## - BUF 1 14.7 15747 -15226.0
## - WAS 1 15.8 15748 -15224.1
## - TEN 1 15.8 15748 -15224.0
## - ATL 1 17.9 15750 -15220.3
## - NYJ 1 18.2 15750 -15219.9
## - PIT 1 19.5 15752 -15217.5
## - NYG 1 19.8 15752 -15217.0
## - CHI 1 19.9 15752 -15217.0
## - CIN 1 20.1 15752 -15216.5
## - KC 1 20.3 15752 -15216.2
## - MIA 1 21.6 15754 -15213.9
## - PHI 1 22.1 15754 -15213.0
## - forty1 1 22.2 15754 -15212.9
## - OAK 1 24.2 15756 -15209.3
## - STL 1 26.7 15759 -15205.1
## - MINN 1 27.9 15760 -15202.8
## - IND 1 28.0 15760 -15202.7
## - ARI 1 28.7 15761 -15201.6
## - DET 1 29.5 15761 -15200.2
## - BAL 1 34.4 15766 -15191.6
## - HOU 1 34.7 15767 -15191.1
## - weight 1 35.2 15767 -15190.2
## - JAC 1 35.2 15767 -15190.2
## - CLE 1 60.2 15792 -15146.7
## - avg_qbtdp_plyr 1 81.2 15813 -15110.2
## - avg_rbry_pos 1 100.4 15832 -15076.8
## - avg_rbry_plyr 1 126.6 15858 -15031.3
## - avg_rectd_plyr 1 5600.4 21332 -6881.9Receiving TD’s
PreProcess:
set.seed(123)
splittdrec <- sample.split(nfl_data$tdrec, SplitRatio = 0.7)
Traintdrec <- subset(nfl_data, split == TRUE)
Testtdrec <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Traintdrec, method = c("center", "scale"))
trainTransformedtdrec <- predict(preProcValues, Traintdrec)
testTransformedtdrec <- predict(preProcValues, Testtdrec)ggpairs:
ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[46:51]))])
tdrecregform <- formula(paste("tdrec ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegRecTD <- lm(tdrecregform, data = trainTransformedtdrec)
summary(linRegRecTD)##
## Call:
## lm(formula = tdrecregform, data = trainTransformedtdrec)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.0021 -0.4352 -0.1339 -0.0007 9.0491
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.581e-16 5.564e-03 0.000 1.0000
## height -1.859e-03 1.080e-02 -0.172 0.8633
## weight 3.922e-03 1.012e-02 0.388 0.6983
## cold_weather -2.811e-03 5.857e-03 -0.480 0.6312
## hot_weather -4.891e-03 5.615e-03 -0.871 0.3837
## home_team_1 1.117e-02 6.054e-03 1.845 0.0651 .
## forty1 3.616e-04 9.602e-03 0.038 0.9700
## vertical1 -4.348e-04 7.383e-03 -0.059 0.9530
## ARI 7.210e-03 7.783e-03 0.926 0.3542
## ATL 1.778e-02 7.821e-03 2.273 0.0230 *
## BAL 1.095e-02 7.827e-03 1.399 0.1618
## BUF 1.508e-02 7.727e-03 1.951 0.0510 .
## CAR 1.471e-02 7.676e-03 1.916 0.0554 .
## CHI 1.662e-02 7.590e-03 2.189 0.0286 *
## CIN 1.403e-02 7.730e-03 1.815 0.0695 .
## CLE 7.259e-03 7.695e-03 0.943 0.3455
## DAL 1.531e-02 7.773e-03 1.970 0.0489 *
## DEN 1.319e-02 7.802e-03 1.691 0.0909 .
## DET 1.178e-02 7.695e-03 1.530 0.1259
## GB 1.357e-02 7.922e-03 1.714 0.0866 .
## HOU 9.462e-03 7.827e-03 1.209 0.2267
## IND 1.545e-02 7.770e-03 1.989 0.0467 *
## JAC 1.234e-02 7.580e-03 1.629 0.1034
## KC 1.290e-02 7.746e-03 1.666 0.0958 .
## MIA 6.369e-03 7.621e-03 0.836 0.4033
## MINN 6.372e-03 7.668e-03 0.831 0.4059
## NE 1.092e-02 8.008e-03 1.364 0.1726
## NOR 2.257e-02 7.983e-03 2.827 0.0047 **
## NYG 1.288e-02 7.803e-03 1.650 0.0989 .
## NYJ 7.421e-03 7.774e-03 0.955 0.3398
## OAK 1.286e-02 7.823e-03 1.643 0.1003
## PHI 6.709e-03 7.581e-03 0.885 0.3762
## PIT 1.512e-02 7.780e-03 1.943 0.0520 .
## SD 1.438e-02 7.635e-03 1.884 0.0596 .
## SEA 8.028e-03 7.923e-03 1.013 0.3110
## STL 5.368e-03 7.712e-03 0.696 0.4864
## TB 1.070e-02 7.640e-03 1.401 0.1612
## TEN 1.366e-02 7.686e-03 1.778 0.0755 .
## WAS 1.131e-02 7.727e-03 1.463 0.1434
## avg_trg_team NA NA NA NA
## avg_rectd_plyr 3.863e-01 7.105e-03 54.366 <2e-16 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr -2.765e-03 8.503e-03 -0.325 0.7450
## avg_rbry_pos 3.315e-03 9.907e-03 0.335 0.7379
## avg_fuml_plyr 1.343e-03 8.219e-03 0.163 0.8702
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -1.978e-03 8.928e-03 -0.222 0.8247
## avg_qbtdp_team NA NA NA NA
## grass_1 -5.577e-03 6.402e-03 -0.871 0.3837
## bad_weather_1 1.094e-02 5.660e-03 1.933 0.0533 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9224 on 27438 degrees of freedom
## Multiple R-squared: 0.1505, Adjusted R-squared: 0.1491
## F-statistic: 108.1 on 45 and 27438 DF, p-value: < 2.2e-16linRegRecTD2 <- update(linRegRecTD, ~. -height-weight-cold_weather-hot_weather-home_team_1
-forty1-is_WR-is_TE-age-vertical1-ARI-BAL-BUF-CAR-CIN-CLE-DAL-DEN-DET-GB
-HOU-IND-JAC-KC-MIA-MINN-NE-NYG-NYJ-OAK-PHI-PIT-SEA-STL-TB-TEN-WAS
-avg_trg_team -avg_tdr_team-avg_rbra_team-avg_rbry_plyr
-avg_rbry_pos-avg_fuml_plyr-avg_fuml_team-avg_qbints_plyr_avg_qbtdp_team
-avg_qbints_team - grass_1-bad_weather_1)
summary(linRegRecTD2)##
## Call:
## lm(formula = tdrec ~ ATL + CHI + NOR + SD + avg_rectd_plyr +
## avg_qbtdp_plyr + avg_qbtdp_team, data = trainTransformedtdrec)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9578 -0.4394 -0.1323 0.0057 9.0814
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.458e-16 5.562e-03 0.000 1.0000
## ATL 3.963e-03 5.688e-03 0.697 0.4860
## CHI 6.058e-03 5.575e-03 1.087 0.2772
## NOR 6.674e-03 6.066e-03 1.100 0.2713
## SD 8.847e-04 5.737e-03 0.154 0.8775
## avg_rectd_plyr 3.840e-01 5.942e-03 64.613 <2e-16 ***
## avg_qbtdp_plyr -1.707e-03 5.877e-03 -0.291 0.7714
## avg_qbtdp_team 1.171e-02 6.388e-03 1.834 0.0667 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9221 on 27476 degrees of freedom
## Multiple R-squared: 0.1499, Adjusted R-squared: 0.1497
## F-statistic: 692.4 on 7 and 27476 DF, p-value: < 2.2e-16linRegRecTD3 <- update(linRegRecTD2, ~. -ATL-CHI-NOR-SD-avg_qbints_plyr-avg_qbints_team)
summary(linRegRecTD3)##
## Call:
## lm(formula = tdrec ~ avg_rectd_plyr + avg_qbtdp_plyr + avg_qbtdp_team,
## data = trainTransformedtdrec)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9629 -0.4373 -0.1342 0.0040 9.0780
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.147e-16 5.562e-03 0.000 1.00000
## avg_rectd_plyr 3.839e-01 5.941e-03 64.611 < 2e-16 ***
## avg_qbtdp_plyr -1.732e-03 5.876e-03 -0.295 0.76822
## avg_qbtdp_team 1.505e-02 5.686e-03 2.647 0.00811 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9221 on 27480 degrees of freedom
## Multiple R-squared: 0.1499, Adjusted R-squared: 0.1498
## F-statistic: 1615 on 3 and 27480 DF, p-value: < 2.2e-16The R2 is worsened in the second model, and the third. (the R2 in general is fairly low)
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
RectdPredicted <- predict(linRegRecTD3, newdata = testTransformedtdrec)
SSErectd <- sum((RectdPredicted - testTransformedtdrec$tdrec)^2)
SSTrectd <- sum((mean(nfl_data$tdrec)-testTransformedtdrec$tdrec)^2)
r2_rectd <- 1 - SSErectd/SSTrectd
r2_rectd## [1] 0.1697301rmse_rectd <- sqrt(SSEtrg/nrow(testTransformedtdrec))
rmse_rectd## [1] 0.7421937Regression plots below
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegRecTD3, which = c(1:3,5))
I would say that it appears that these charts do not like the prediction. Touchdowns are infrequent and random/unpredictable. If a receiver has an amazing season and gets 100 receptions, if they had 10 Tds it would be an All-pro year for them.
Additional summary statistics
confint(linRegRecTD3)## 2.5 % 97.5 %
## (Intercept) -0.010901714 0.01090171
## avg_rectd_plyr 0.372215276 0.39550490
## avg_qbtdp_plyr -0.013249830 0.00978614
## avg_qbtdp_team 0.003908858 0.02619924coef(summary(linRegRecTD3))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.146925e-16 0.005561956 -9.253804e-14 1.000000000
## avg_rectd_plyr 3.838601e-01 0.005941078 6.461119e+01 0.000000000
## avg_qbtdp_plyr -1.731845e-03 0.005876372 -2.947133e-01 0.768215113
## avg_qbtdp_team 1.505405e-02 0.005686176 2.647482e+00 0.008113993anova(linRegRecTD3)## Analysis of Variance Table
##
## Response: tdrec
## Df Sum Sq Mean Sq F value Pr(>F)
## avg_rectd_plyr 1 4112.8 4112.8 4837.2842 < 2.2e-16 ***
## avg_qbtdp_plyr 1 0.0 0.0 0.0023 0.961434
## avg_qbtdp_team 1 6.0 6.0 7.0092 0.008114 **
## Residuals 27480 23364.2 0.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_tdrec <- step(lm(tdrecregform, data = trainTransformedtdrec), direction = "backward")## Start: AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - forty1 1 0.00 23346 -4394.9
## - vertical1 1 0.00 23346 -4394.9
## - avg_fuml_plyr 1 0.02 23346 -4394.9
## - height 1 0.03 23346 -4394.9
## - avg_qbtdp_plyr 1 0.04 23346 -4394.9
## - avg_rbry_plyr 1 0.09 23346 -4394.8
## - avg_rbry_pos 1 0.10 23346 -4394.8
## - weight 1 0.13 23346 -4394.8
## - cold_weather 1 0.20 23346 -4394.7
## - STL 1 0.41 23346 -4394.4
## - MINN 1 0.59 23347 -4394.2
## - MIA 1 0.59 23347 -4394.2
## - hot_weather 1 0.65 23347 -4394.2
## - grass_1 1 0.65 23347 -4394.2
## - PHI 1 0.67 23347 -4394.1
## - ARI 1 0.73 23347 -4394.1
## - CLE 1 0.76 23347 -4394.0
## - NYJ 1 0.78 23347 -4394.0
## - SEA 1 0.87 23347 -4393.9
## - HOU 1 1.24 23347 -4393.5
## - NE 1 1.58 23348 -4393.1
## - BAL 1 1.67 23348 -4393.0
## - TB 1 1.67 23348 -4392.9
## <none> 23346 -4392.9
## - WAS 1 1.82 23348 -4392.8
## - DET 1 1.99 23348 -4392.6
## - JAC 1 2.26 23348 -4392.3
## - OAK 1 2.30 23348 -4392.2
## - NYG 1 2.32 23348 -4392.2
## - KC 1 2.36 23348 -4392.1
## - DEN 1 2.43 23348 -4392.1
## - GB 1 2.50 23348 -4392.0
## - TEN 1 2.69 23349 -4391.8
## - CIN 1 2.80 23349 -4391.6
## - home_team_1 1 2.89 23349 -4391.5
## - SD 1 3.02 23349 -4391.4
## - CAR 1 3.12 23349 -4391.2
## - bad_weather_1 1 3.18 23349 -4391.2
## - PIT 1 3.21 23349 -4391.1
## - BUF 1 3.24 23349 -4391.1
## - DAL 1 3.30 23349 -4391.0
## - IND 1 3.37 23349 -4391.0
## - CHI 1 4.08 23350 -4390.1
## - ATL 1 4.40 23350 -4389.7
## - NOR 1 6.80 23353 -4386.9
## - avg_rectd_plyr 1 2514.88 25861 -1583.1
##
## Step: AIC=-4394.91
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 0.01 23346 -4396.9
## - avg_fuml_plyr 1 0.02 23346 -4396.9
## - height 1 0.03 23346 -4396.9
## - avg_qbtdp_plyr 1 0.04 23346 -4396.9
## - avg_rbry_pos 1 0.09 23346 -4396.8
## - avg_rbry_plyr 1 0.10 23346 -4396.8
## - weight 1 0.16 23346 -4396.7
## - cold_weather 1 0.20 23346 -4396.7
## - STL 1 0.41 23346 -4396.4
## - MINN 1 0.59 23347 -4396.2
## - MIA 1 0.59 23347 -4396.2
## - hot_weather 1 0.65 23347 -4396.2
## - grass_1 1 0.65 23347 -4396.2
## - PHI 1 0.67 23347 -4396.1
## - ARI 1 0.73 23347 -4396.1
## - CLE 1 0.76 23347 -4396.0
## - NYJ 1 0.78 23347 -4396.0
## - SEA 1 0.87 23347 -4395.9
## - HOU 1 1.25 23347 -4395.4
## - NE 1 1.60 23348 -4395.0
## - BAL 1 1.66 23348 -4395.0
## - TB 1 1.67 23348 -4394.9
## <none> 23346 -4394.9
## - WAS 1 1.82 23348 -4394.8
## - DET 1 1.99 23348 -4394.6
## - JAC 1 2.26 23348 -4394.3
## - OAK 1 2.30 23348 -4394.2
## - NYG 1 2.32 23348 -4394.2
## - KC 1 2.36 23348 -4394.1
## - DEN 1 2.43 23348 -4394.0
## - GB 1 2.50 23348 -4394.0
## - TEN 1 2.69 23349 -4393.7
## - CIN 1 2.80 23349 -4393.6
## - home_team_1 1 2.89 23349 -4393.5
## - SD 1 3.02 23349 -4393.4
## - CAR 1 3.12 23349 -4393.2
## - bad_weather_1 1 3.18 23349 -4393.2
## - PIT 1 3.21 23349 -4393.1
## - BUF 1 3.24 23349 -4393.1
## - DAL 1 3.30 23349 -4393.0
## - IND 1 3.36 23349 -4393.0
## - CHI 1 4.08 23350 -4392.1
## - ATL 1 4.40 23350 -4391.7
## - NOR 1 6.80 23353 -4388.9
## - avg_rectd_plyr 1 2556.93 25903 -1540.5
##
## Step: AIC=-4396.91
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR +
## NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_fuml_plyr 1 0.02 23346 -4398.9
## - height 1 0.03 23346 -4398.9
## - avg_qbtdp_plyr 1 0.04 23346 -4398.9
## - avg_rbry_pos 1 0.10 23346 -4398.8
## - avg_rbry_plyr 1 0.10 23346 -4398.8
## - weight 1 0.18 23346 -4398.7
## - cold_weather 1 0.20 23346 -4398.7
## - STL 1 0.42 23346 -4398.4
## - MINN 1 0.59 23347 -4398.2
## - MIA 1 0.60 23347 -4398.2
## - hot_weather 1 0.65 23347 -4398.1
## - grass_1 1 0.65 23347 -4398.1
## - PHI 1 0.67 23347 -4398.1
## - ARI 1 0.73 23347 -4398.0
## - CLE 1 0.76 23347 -4398.0
## - NYJ 1 0.77 23347 -4398.0
## - SEA 1 0.87 23347 -4397.9
## - HOU 1 1.25 23347 -4397.4
## - NE 1 1.63 23348 -4397.0
## - BAL 1 1.67 23348 -4396.9
## - TB 1 1.68 23348 -4396.9
## <none> 23346 -4396.9
## - WAS 1 1.82 23348 -4396.8
## - DET 1 1.99 23348 -4396.6
## - JAC 1 2.26 23348 -4396.3
## - OAK 1 2.30 23348 -4396.2
## - NYG 1 2.33 23348 -4396.2
## - KC 1 2.36 23348 -4396.1
## - DEN 1 2.43 23348 -4396.0
## - GB 1 2.51 23348 -4395.9
## - TEN 1 2.69 23349 -4395.7
## - CIN 1 2.82 23349 -4395.6
## - home_team_1 1 2.89 23349 -4395.5
## - SD 1 3.04 23349 -4395.3
## - CAR 1 3.12 23349 -4395.2
## - bad_weather_1 1 3.18 23349 -4395.2
## - PIT 1 3.22 23349 -4395.1
## - BUF 1 3.25 23349 -4395.1
## - DAL 1 3.31 23349 -4395.0
## - IND 1 3.36 23349 -4394.9
## - CHI 1 4.09 23350 -4394.1
## - ATL 1 4.44 23350 -4393.7
## - NOR 1 6.80 23353 -4390.9
## - avg_rectd_plyr 1 2604.08 25950 -1492.5
##
## Step: AIC=-4398.88
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR +
## NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_qbtdp_plyr 1 0.01 23346 -4400.9
## - height 1 0.02 23346 -4400.9
## - avg_rbry_plyr 1 0.08 23346 -4400.8
## - avg_rbry_pos 1 0.10 23346 -4400.8
## - weight 1 0.17 23346 -4400.7
## - cold_weather 1 0.20 23346 -4400.6
## - STL 1 0.42 23346 -4400.4
## - MINN 1 0.59 23347 -4400.2
## - MIA 1 0.60 23347 -4400.2
## - hot_weather 1 0.65 23347 -4400.1
## - grass_1 1 0.65 23347 -4400.1
## - PHI 1 0.68 23347 -4400.1
## - ARI 1 0.74 23347 -4400.0
## - CLE 1 0.77 23347 -4400.0
## - NYJ 1 0.78 23347 -4400.0
## - SEA 1 0.87 23347 -4399.9
## - HOU 1 1.25 23347 -4399.4
## - NE 1 1.61 23348 -4399.0
## - BAL 1 1.66 23348 -4398.9
## - TB 1 1.69 23348 -4398.9
## <none> 23346 -4398.9
## - WAS 1 1.83 23348 -4398.7
## - DET 1 2.00 23348 -4398.5
## - JAC 1 2.25 23348 -4398.2
## - OAK 1 2.30 23348 -4398.2
## - NYG 1 2.34 23348 -4398.1
## - KC 1 2.37 23348 -4398.1
## - DEN 1 2.44 23348 -4398.0
## - GB 1 2.50 23348 -4397.9
## - TEN 1 2.70 23349 -4397.7
## - CIN 1 2.82 23349 -4397.6
## - home_team_1 1 2.90 23349 -4397.5
## - SD 1 3.05 23349 -4397.3
## - CAR 1 3.12 23349 -4397.2
## - bad_weather_1 1 3.18 23349 -4397.1
## - PIT 1 3.23 23349 -4397.1
## - BUF 1 3.26 23349 -4397.0
## - DAL 1 3.31 23349 -4397.0
## - IND 1 3.36 23349 -4396.9
## - CHI 1 4.12 23350 -4396.0
## - ATL 1 4.42 23350 -4395.7
## - NOR 1 6.79 23353 -4392.9
## - avg_rectd_plyr 1 2605.85 25952 -1492.6
##
## Step: AIC=-4400.86
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR +
## NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - height 1 0.05 23346 -4402.8
## - avg_rbry_plyr 1 0.08 23346 -4402.8
## - avg_rbry_pos 1 0.09 23346 -4402.8
## - cold_weather 1 0.20 23346 -4402.6
## - weight 1 0.21 23346 -4402.6
## - STL 1 0.43 23346 -4402.4
## - MINN 1 0.60 23347 -4402.2
## - MIA 1 0.60 23347 -4402.1
## - hot_weather 1 0.64 23347 -4402.1
## - grass_1 1 0.65 23347 -4402.1
## - PHI 1 0.68 23347 -4402.1
## - ARI 1 0.74 23347 -4402.0
## - CLE 1 0.77 23347 -4401.9
## - NYJ 1 0.79 23347 -4401.9
## - SEA 1 0.86 23347 -4401.8
## - HOU 1 1.26 23347 -4401.4
## - NE 1 1.60 23348 -4401.0
## - BAL 1 1.67 23348 -4400.9
## - TB 1 1.69 23348 -4400.9
## <none> 23346 -4400.9
## - WAS 1 1.83 23348 -4400.7
## - DET 1 2.00 23348 -4400.5
## - JAC 1 2.26 23348 -4400.2
## - OAK 1 2.31 23348 -4400.1
## - NYG 1 2.33 23348 -4400.1
## - KC 1 2.38 23348 -4400.1
## - DEN 1 2.43 23348 -4400.0
## - GB 1 2.49 23348 -4399.9
## - TEN 1 2.71 23349 -4399.7
## - CIN 1 2.82 23349 -4399.5
## - home_team_1 1 2.90 23349 -4399.4
## - SD 1 3.04 23349 -4399.3
## - CAR 1 3.12 23349 -4399.2
## - bad_weather_1 1 3.18 23349 -4399.1
## - PIT 1 3.23 23349 -4399.1
## - BUF 1 3.28 23349 -4399.0
## - DAL 1 3.30 23349 -4399.0
## - IND 1 3.35 23349 -4398.9
## - CHI 1 4.13 23350 -4398.0
## - ATL 1 4.41 23350 -4397.7
## - NOR 1 6.77 23353 -4394.9
## - avg_rectd_plyr 1 3038.70 26385 -1039.9
##
## Step: AIC=-4402.81
## tdrec ~ weight + cold_weather + hot_weather + home_team_1 + ARI +
## ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_rbry_plyr 1 0.08 23346 -4404.7
## - cold_weather 1 0.20 23346 -4404.6
## - weight 1 0.21 23346 -4404.6
## - avg_rbry_pos 1 0.23 23346 -4404.5
## - STL 1 0.42 23346 -4404.3
## - MINN 1 0.58 23347 -4404.1
## - MIA 1 0.60 23347 -4404.1
## - hot_weather 1 0.65 23347 -4404.0
## - grass_1 1 0.65 23347 -4404.0
## - PHI 1 0.68 23347 -4404.0
## - ARI 1 0.73 23347 -4403.9
## - CLE 1 0.77 23347 -4403.9
## - NYJ 1 0.78 23347 -4403.9
## - SEA 1 0.86 23347 -4403.8
## - HOU 1 1.24 23347 -4403.3
## - NE 1 1.60 23348 -4402.9
## - BAL 1 1.66 23348 -4402.9
## - TB 1 1.67 23348 -4402.8
## <none> 23346 -4402.8
## - WAS 1 1.85 23348 -4402.6
## - DET 1 1.98 23348 -4402.5
## - JAC 1 2.25 23348 -4402.2
## - OAK 1 2.28 23348 -4402.1
## - NYG 1 2.31 23348 -4402.1
## - KC 1 2.36 23348 -4402.0
## - DEN 1 2.42 23348 -4402.0
## - GB 1 2.48 23349 -4401.9
## - TEN 1 2.69 23349 -4401.6
## - CIN 1 2.79 23349 -4401.5
## - home_team_1 1 2.90 23349 -4401.4
## - SD 1 3.01 23349 -4401.3
## - CAR 1 3.12 23349 -4401.1
## - bad_weather_1 1 3.18 23349 -4401.1
## - PIT 1 3.21 23349 -4401.0
## - BUF 1 3.25 23349 -4401.0
## - DAL 1 3.28 23349 -4400.9
## - IND 1 3.36 23349 -4400.9
## - CHI 1 4.09 23350 -4400.0
## - ATL 1 4.41 23350 -4399.6
## - NOR 1 6.75 23353 -4396.9
## - avg_rectd_plyr 1 3044.09 26390 -1036.3
##
## Step: AIC=-4404.71
## tdrec ~ weight + cold_weather + hot_weather + home_team_1 + ARI +
## ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_rbry_pos 1 0.15 23346 -4406.5
## - cold_weather 1 0.19 23346 -4406.5
## - weight 1 0.23 23346 -4406.4
## - STL 1 0.43 23347 -4406.2
## - MINN 1 0.58 23347 -4406.0
## - MIA 1 0.61 23347 -4406.0
## - grass_1 1 0.65 23347 -4405.9
## - hot_weather 1 0.65 23347 -4405.9
## - PHI 1 0.67 23347 -4405.9
## - ARI 1 0.74 23347 -4405.8
## - NYJ 1 0.78 23347 -4405.8
## - CLE 1 0.78 23347 -4405.8
## - SEA 1 0.86 23347 -4405.7
## - HOU 1 1.24 23347 -4405.2
## - NE 1 1.61 23348 -4404.8
## - BAL 1 1.68 23348 -4404.7
## - TB 1 1.69 23348 -4404.7
## <none> 23346 -4404.7
## - WAS 1 1.86 23348 -4404.5
## - DET 1 2.02 23348 -4404.3
## - JAC 1 2.27 23348 -4404.0
## - OAK 1 2.31 23348 -4404.0
## - NYG 1 2.34 23348 -4404.0
## - KC 1 2.37 23348 -4403.9
## - DEN 1 2.44 23349 -4403.8
## - GB 1 2.49 23349 -4403.8
## - TEN 1 2.71 23349 -4403.5
## - CIN 1 2.80 23349 -4403.4
## - home_team_1 1 2.90 23349 -4403.3
## - SD 1 3.04 23349 -4403.1
## - CAR 1 3.11 23349 -4403.0
## - bad_weather_1 1 3.17 23349 -4403.0
## - PIT 1 3.22 23349 -4402.9
## - BUF 1 3.25 23349 -4402.9
## - DAL 1 3.29 23349 -4402.8
## - IND 1 3.37 23349 -4402.7
## - CHI 1 4.09 23350 -4401.9
## - ATL 1 4.45 23351 -4401.5
## - NOR 1 6.81 23353 -4398.7
## - avg_rectd_plyr 1 3050.16 26396 -1031.9
##
## Step: AIC=-4406.53
## tdrec ~ weight + cold_weather + hot_weather + home_team_1 + ARI +
## ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS +
## avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - cold_weather 1 0.2 23346 -4408.3
## - weight 1 0.2 23346 -4408.3
## - STL 1 0.4 23347 -4408.0
## - MINN 1 0.6 23347 -4407.9
## - MIA 1 0.6 23347 -4407.8
## - grass_1 1 0.6 23347 -4407.8
## - hot_weather 1 0.7 23347 -4407.8
## - PHI 1 0.7 23347 -4407.7
## - ARI 1 0.7 23347 -4407.7
## - CLE 1 0.8 23347 -4407.6
## - NYJ 1 0.8 23347 -4407.6
## - SEA 1 0.9 23347 -4407.5
## - HOU 1 1.2 23348 -4407.1
## - NE 1 1.6 23348 -4406.6
## - BAL 1 1.7 23348 -4406.6
## - TB 1 1.7 23348 -4406.6
## <none> 23346 -4406.5
## - WAS 1 1.8 23348 -4406.4
## - DET 1 2.0 23348 -4406.1
## - JAC 1 2.3 23349 -4405.9
## - OAK 1 2.3 23349 -4405.8
## - NYG 1 2.3 23349 -4405.8
## - KC 1 2.4 23349 -4405.7
## - DEN 1 2.4 23349 -4405.7
## - GB 1 2.5 23349 -4405.6
## - TEN 1 2.7 23349 -4405.4
## - CIN 1 2.8 23349 -4405.3
## - home_team_1 1 2.9 23349 -4405.1
## - SD 1 3.1 23349 -4404.9
## - CAR 1 3.1 23349 -4404.9
## - bad_weather_1 1 3.2 23349 -4404.8
## - PIT 1 3.2 23349 -4404.7
## - BUF 1 3.3 23350 -4404.7
## - DAL 1 3.3 23350 -4404.7
## - IND 1 3.4 23350 -4404.6
## - CHI 1 4.1 23350 -4403.7
## - ATL 1 4.5 23351 -4403.3
## - NOR 1 6.9 23353 -4400.4
## - avg_rectd_plyr 1 3957.8 27304 -104.6
##
## Step: AIC=-4408.31
## tdrec ~ weight + hot_weather + home_team_1 + ARI + ATL + BAL +
## BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU +
## IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + PIT + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - weight 1 0.2 23347 -4410.0
## - STL 1 0.4 23347 -4409.8
## - MINN 1 0.5 23347 -4409.7
## - MIA 1 0.6 23347 -4409.6
## - hot_weather 1 0.6 23347 -4409.6
## - PHI 1 0.6 23347 -4409.6
## - grass_1 1 0.7 23347 -4409.5
## - CLE 1 0.7 23347 -4409.5
## - ARI 1 0.7 23347 -4409.5
## - NYJ 1 0.7 23347 -4409.4
## - SEA 1 0.8 23347 -4409.4
## - HOU 1 1.2 23348 -4408.9
## - NE 1 1.6 23348 -4408.5
## - BAL 1 1.6 23348 -4408.4
## - TB 1 1.7 23348 -4408.3
## <none> 23346 -4408.3
## - WAS 1 1.8 23348 -4408.2
## - DET 1 2.0 23349 -4407.9
## - NYG 1 2.3 23349 -4407.6
## - JAC 1 2.3 23349 -4407.6
## - KC 1 2.3 23349 -4407.6
## - OAK 1 2.3 23349 -4407.6
## - DEN 1 2.4 23349 -4407.5
## - GB 1 2.4 23349 -4407.5
## - TEN 1 2.7 23349 -4407.2
## - CIN 1 2.7 23349 -4407.1
## - home_team_1 1 2.8 23349 -4407.0
## - bad_weather_1 1 3.0 23350 -4406.7
## - SD 1 3.1 23350 -4406.7
## - CAR 1 3.1 23350 -4406.7
## - PIT 1 3.1 23350 -4406.6
## - BUF 1 3.2 23350 -4406.6
## - DAL 1 3.3 23350 -4406.4
## - IND 1 3.3 23350 -4406.4
## - CHI 1 4.0 23350 -4405.6
## - ATL 1 4.5 23351 -4405.0
## - NOR 1 6.9 23353 -4402.2
## - avg_rectd_plyr 1 3958.6 27305 -105.5
##
## Step: AIC=-4410.04
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT +
## SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - STL 1 0.4 23347 -4411.6
## - MINN 1 0.5 23347 -4411.4
## - MIA 1 0.6 23347 -4411.3
## - PHI 1 0.6 23347 -4411.3
## - hot_weather 1 0.6 23347 -4411.3
## - grass_1 1 0.7 23347 -4411.2
## - CLE 1 0.7 23347 -4411.2
## - NYJ 1 0.7 23347 -4411.2
## - ARI 1 0.7 23347 -4411.2
## - SEA 1 0.8 23347 -4411.1
## - HOU 1 1.2 23348 -4410.6
## - NE 1 1.6 23348 -4410.2
## - BAL 1 1.6 23348 -4410.1
## <none> 23347 -4410.0
## - TB 1 1.7 23348 -4410.0
## - WAS 1 1.8 23348 -4410.0
## - DET 1 2.0 23349 -4409.6
## - JAC 1 2.3 23349 -4409.4
## - KC 1 2.3 23349 -4409.4
## - NYG 1 2.3 23349 -4409.4
## - OAK 1 2.3 23349 -4409.3
## - DEN 1 2.3 23349 -4409.3
## - GB 1 2.4 23349 -4409.2
## - TEN 1 2.6 23349 -4408.9
## - CIN 1 2.7 23349 -4408.9
## - home_team_1 1 2.8 23349 -4408.7
## - bad_weather_1 1 3.1 23350 -4408.5
## - SD 1 3.1 23350 -4408.4
## - CAR 1 3.1 23350 -4408.4
## - PIT 1 3.1 23350 -4408.4
## - BUF 1 3.1 23350 -4408.3
## - DAL 1 3.3 23350 -4408.2
## - IND 1 3.3 23350 -4408.2
## - CHI 1 4.0 23351 -4407.4
## - ATL 1 4.5 23351 -4406.8
## - NOR 1 6.9 23354 -4404.0
## - avg_rectd_plyr 1 3958.4 27305 -107.5
##
## Step: AIC=-4411.57
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT +
## SD + SEA + TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MINN 1 0.2 23347 -4413.3
## - MIA 1 0.3 23347 -4413.2
## - PHI 1 0.3 23347 -4413.2
## - CLE 1 0.4 23347 -4413.1
## - ARI 1 0.4 23347 -4413.1
## - NYJ 1 0.4 23347 -4413.1
## - SEA 1 0.4 23348 -4413.1
## - hot_weather 1 0.6 23348 -4412.9
## - grass_1 1 0.8 23348 -4412.7
## - HOU 1 0.9 23348 -4412.6
## - NE 1 1.2 23348 -4412.2
## - BAL 1 1.2 23348 -4412.1
## - TB 1 1.3 23348 -4412.0
## - WAS 1 1.4 23348 -4412.0
## - DET 1 1.6 23349 -4411.6
## <none> 23347 -4411.6
## - JAC 1 1.9 23349 -4411.4
## - KC 1 1.9 23349 -4411.4
## - NYG 1 1.9 23349 -4411.3
## - OAK 1 1.9 23349 -4411.3
## - DEN 1 2.0 23349 -4411.3
## - GB 1 2.1 23349 -4411.2
## - TEN 1 2.3 23349 -4410.9
## - CIN 1 2.3 23349 -4410.9
## - home_team_1 1 2.6 23350 -4410.5
## - SD 1 2.7 23350 -4410.4
## - CAR 1 2.7 23350 -4410.4
## - PIT 1 2.7 23350 -4410.3
## - BUF 1 2.8 23350 -4410.3
## - DAL 1 3.0 23350 -4410.1
## - IND 1 3.0 23350 -4410.1
## - bad_weather_1 1 3.0 23350 -4410.0
## - CHI 1 3.7 23351 -4409.2
## - ATL 1 4.3 23351 -4408.5
## - NOR 1 7.1 23354 -4405.2
## - avg_rectd_plyr 1 3959.9 27307 -107.7
##
## Step: AIC=-4413.3
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MIA + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.2 23347 -4415.1
## - PHI 1 0.2 23348 -4415.1
## - CLE 1 0.2 23348 -4415.0
## - NYJ 1 0.2 23348 -4415.0
## - ARI 1 0.2 23348 -4415.0
## - SEA 1 0.3 23348 -4415.0
## - hot_weather 1 0.6 23348 -4414.6
## - HOU 1 0.7 23348 -4414.5
## - grass_1 1 0.8 23348 -4414.3
## - NE 1 0.9 23348 -4414.2
## - BAL 1 1.0 23348 -4414.1
## - TB 1 1.1 23348 -4414.0
## - WAS 1 1.2 23348 -4413.9
## - DET 1 1.4 23349 -4413.6
## - JAC 1 1.7 23349 -4413.4
## - KC 1 1.7 23349 -4413.3
## - NYG 1 1.7 23349 -4413.3
## - OAK 1 1.7 23349 -4413.3
## <none> 23347 -4413.3
## - DEN 1 1.7 23349 -4413.3
## - GB 1 1.8 23349 -4413.2
## - TEN 1 2.0 23349 -4412.9
## - CIN 1 2.1 23349 -4412.9
## - SD 1 2.5 23350 -4412.4
## - CAR 1 2.5 23350 -4412.4
## - PIT 1 2.5 23350 -4412.3
## - BUF 1 2.6 23350 -4412.3
## - home_team_1 1 2.7 23350 -4412.1
## - DAL 1 2.7 23350 -4412.1
## - IND 1 2.8 23350 -4412.1
## - bad_weather_1 1 3.0 23350 -4411.8
## - CHI 1 3.5 23351 -4411.2
## - ATL 1 4.1 23351 -4410.4
## - NOR 1 7.1 23354 -4407.0
## - avg_rectd_plyr 1 3960.1 27307 -109.2
##
## Step: AIC=-4415.11
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PHI 1 0.1 23348 -4417.0
## - CLE 1 0.2 23348 -4416.9
## - NYJ 1 0.2 23348 -4416.9
## - ARI 1 0.2 23348 -4416.9
## - SEA 1 0.2 23348 -4416.9
## - HOU 1 0.5 23348 -4416.5
## - hot_weather 1 0.6 23348 -4416.4
## - grass_1 1 0.8 23348 -4416.2
## - NE 1 0.8 23348 -4416.2
## - BAL 1 0.9 23348 -4416.1
## - TB 1 0.9 23348 -4416.0
## - WAS 1 1.0 23348 -4415.9
## - DET 1 1.3 23349 -4415.6
## - JAC 1 1.5 23349 -4415.3
## - KC 1 1.5 23349 -4415.3
## - NYG 1 1.5 23349 -4415.3
## - OAK 1 1.5 23349 -4415.3
## - DEN 1 1.6 23349 -4415.3
## - GB 1 1.7 23349 -4415.2
## <none> 23347 -4415.1
## - TEN 1 1.9 23349 -4414.9
## - CIN 1 1.9 23349 -4414.9
## - SD 1 2.3 23350 -4414.4
## - CAR 1 2.3 23350 -4414.4
## - PIT 1 2.4 23350 -4414.3
## - BUF 1 2.4 23350 -4414.3
## - DAL 1 2.6 23350 -4414.1
## - IND 1 2.6 23350 -4414.1
## - home_team_1 1 2.8 23350 -4413.8
## - bad_weather_1 1 3.0 23350 -4413.6
## - CHI 1 3.3 23351 -4413.2
## - ATL 1 4.0 23351 -4412.4
## - NOR 1 7.0 23354 -4408.9
## - avg_rectd_plyr 1 3962.7 27310 -108.4
##
## Step: AIC=-4416.98
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + NE + NOR + NYG + NYJ + OAK + PIT + SD + SEA + TB + TEN +
## WAS + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CLE 1 0.1 23348 -4418.8
## - NYJ 1 0.1 23348 -4418.8
## - ARI 1 0.1 23348 -4418.8
## - SEA 1 0.1 23348 -4418.8
## - HOU 1 0.5 23348 -4418.4
## - hot_weather 1 0.6 23348 -4418.2
## - NE 1 0.7 23348 -4418.1
## - grass_1 1 0.8 23348 -4418.1
## - BAL 1 0.8 23348 -4418.1
## - TB 1 0.9 23348 -4418.0
## - WAS 1 0.9 23349 -4417.9
## - DET 1 1.2 23349 -4417.6
## - JAC 1 1.4 23349 -4417.3
## - KC 1 1.4 23349 -4417.3
## - NYG 1 1.4 23349 -4417.3
## - OAK 1 1.4 23349 -4417.3
## - DEN 1 1.5 23349 -4417.3
## - GB 1 1.6 23349 -4417.1
## <none> 23348 -4417.0
## - TEN 1 1.8 23349 -4416.9
## - CIN 1 1.8 23349 -4416.9
## - SD 1 2.2 23350 -4416.4
## - CAR 1 2.2 23350 -4416.4
## - PIT 1 2.2 23350 -4416.3
## - BUF 1 2.3 23350 -4416.3
## - DAL 1 2.5 23350 -4416.1
## - IND 1 2.5 23350 -4416.1
## - home_team_1 1 2.8 23350 -4415.7
## - bad_weather_1 1 3.0 23351 -4415.4
## - CHI 1 3.2 23351 -4415.2
## - ATL 1 3.9 23351 -4414.4
## - NOR 1 6.9 23355 -4410.8
## - avg_rectd_plyr 1 3965.2 27313 -107.8
##
## Step: AIC=-4418.85
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR +
## CHI + CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## NE + NOR + NYG + NYJ + OAK + PIT + SD + SEA + TB + TEN +
## WAS + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NYJ 1 0.1 23348 -4420.8
## - ARI 1 0.1 23348 -4420.7
## - SEA 1 0.1 23348 -4420.7
## - HOU 1 0.4 23348 -4420.4
## - hot_weather 1 0.6 23348 -4420.1
## - NE 1 0.6 23348 -4420.1
## - BAL 1 0.7 23348 -4420.0
## - grass_1 1 0.7 23348 -4420.0
## - TB 1 0.8 23348 -4419.9
## - WAS 1 0.8 23349 -4419.9
## - DET 1 1.1 23349 -4419.6
## - KC 1 1.3 23349 -4419.3
## - JAC 1 1.3 23349 -4419.3
## - NYG 1 1.3 23349 -4419.3
## - OAK 1 1.3 23349 -4419.3
## - DEN 1 1.4 23349 -4419.2
## - GB 1 1.5 23349 -4419.1
## - TEN 1 1.7 23349 -4418.9
## <none> 23348 -4418.8
## - CIN 1 1.7 23349 -4418.8
## - SD 1 2.1 23350 -4418.4
## - CAR 1 2.1 23350 -4418.3
## - PIT 1 2.1 23350 -4418.3
## - BUF 1 2.2 23350 -4418.2
## - DAL 1 2.4 23350 -4418.1
## - IND 1 2.4 23350 -4418.0
## - home_team_1 1 2.8 23351 -4417.5
## - bad_weather_1 1 3.1 23351 -4417.3
## - CHI 1 3.1 23351 -4417.2
## - ATL 1 3.8 23351 -4416.4
## - NOR 1 6.8 23355 -4412.8
## - avg_rectd_plyr 1 3967.5 27315 -107.3
##
## Step: AIC=-4420.75
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR +
## CHI + CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## NE + NOR + NYG + OAK + PIT + SD + SEA + TB + TEN + WAS +
## avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ARI 1 0.1 23348 -4422.7
## - SEA 1 0.1 23348 -4422.7
## - HOU 1 0.4 23348 -4422.3
## - NE 1 0.6 23348 -4422.1
## - hot_weather 1 0.6 23348 -4422.0
## - BAL 1 0.6 23348 -4422.0
## - TB 1 0.7 23349 -4421.9
## - WAS 1 0.8 23349 -4421.8
## - grass_1 1 0.8 23349 -4421.8
## - DET 1 1.0 23349 -4421.5
## - KC 1 1.2 23349 -4421.3
## - JAC 1 1.2 23349 -4421.3
## - NYG 1 1.2 23349 -4421.3
## - OAK 1 1.3 23349 -4421.3
## - DEN 1 1.3 23349 -4421.2
## - GB 1 1.4 23349 -4421.1
## - TEN 1 1.6 23349 -4420.9
## - CIN 1 1.6 23349 -4420.8
## <none> 23348 -4420.8
## - SD 1 2.0 23350 -4420.4
## - CAR 1 2.0 23350 -4420.3
## - PIT 1 2.1 23350 -4420.3
## - BUF 1 2.1 23350 -4420.2
## - DAL 1 2.3 23350 -4420.1
## - IND 1 2.3 23350 -4420.0
## - home_team_1 1 2.9 23351 -4419.4
## - CHI 1 3.0 23351 -4419.2
## - bad_weather_1 1 3.1 23351 -4419.1
## - ATL 1 3.7 23351 -4418.4
## - NOR 1 6.8 23355 -4414.8
## - avg_rectd_plyr 1 3967.5 27315 -109.2
##
## Step: AIC=-4422.67
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI +
## CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC + NE +
## NOR + NYG + OAK + PIT + SD + SEA + TB + TEN + WAS + avg_rectd_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.1 23348 -4424.6
## - HOU 1 0.3 23348 -4424.3
## - NE 1 0.5 23348 -4424.0
## - BAL 1 0.6 23348 -4424.0
## - hot_weather 1 0.6 23348 -4423.9
## - TB 1 0.7 23349 -4423.9
## - WAS 1 0.7 23349 -4423.8
## - grass_1 1 0.8 23349 -4423.7
## - DET 1 1.0 23349 -4423.5
## - KC 1 1.2 23349 -4423.3
## - JAC 1 1.2 23349 -4423.3
## - NYG 1 1.2 23349 -4423.3
## - OAK 1 1.2 23349 -4423.2
## - DEN 1 1.2 23349 -4423.2
## - GB 1 1.3 23349 -4423.1
## - TEN 1 1.5 23349 -4422.9
## - CIN 1 1.6 23349 -4422.8
## <none> 23348 -4422.7
## - SD 1 2.0 23350 -4422.4
## - CAR 1 2.0 23350 -4422.3
## - PIT 1 2.0 23350 -4422.3
## - BUF 1 2.1 23350 -4422.2
## - DAL 1 2.2 23350 -4422.1
## - IND 1 2.2 23350 -4422.0
## - home_team_1 1 2.8 23351 -4421.4
## - CHI 1 2.9 23351 -4421.2
## - bad_weather_1 1 3.1 23351 -4421.1
## - ATL 1 3.6 23351 -4420.4
## - NOR 1 6.7 23355 -4416.8
## - avg_rectd_plyr 1 3968.0 27316 -110.7
##
## Step: AIC=-4424.6
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI +
## CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC + NE +
## NOR + NYG + OAK + PIT + SD + TB + TEN + WAS + avg_rectd_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - HOU 1 0.3 23348 -4426.3
## - NE 1 0.5 23348 -4426.0
## - BAL 1 0.6 23348 -4425.9
## - hot_weather 1 0.6 23349 -4425.9
## - TB 1 0.6 23349 -4425.8
## - WAS 1 0.7 23349 -4425.8
## - grass_1 1 0.9 23349 -4425.6
## - DET 1 0.9 23349 -4425.5
## - KC 1 1.1 23349 -4425.3
## - NYG 1 1.1 23349 -4425.3
## - JAC 1 1.1 23349 -4425.3
## - OAK 1 1.2 23349 -4425.2
## - DEN 1 1.2 23349 -4425.2
## - GB 1 1.3 23349 -4425.1
## - TEN 1 1.5 23349 -4424.9
## - CIN 1 1.5 23349 -4424.8
## <none> 23348 -4424.6
## - SD 1 1.9 23350 -4424.3
## - CAR 1 1.9 23350 -4424.3
## - PIT 1 2.0 23350 -4424.3
## - BUF 1 2.0 23350 -4424.2
## - DAL 1 2.2 23350 -4424.1
## - IND 1 2.2 23350 -4424.0
## - home_team_1 1 2.9 23351 -4423.2
## - CHI 1 2.9 23351 -4423.2
## - bad_weather_1 1 3.1 23351 -4423.0
## - ATL 1 3.5 23351 -4422.4
## - NOR 1 6.6 23355 -4418.8
## - avg_rectd_plyr 1 3971.0 27319 -109.6
##
## Step: AIC=-4426.25
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI +
## CIN + DAL + DEN + DET + GB + IND + JAC + KC + NE + NOR +
## NYG + OAK + PIT + SD + TB + TEN + WAS + avg_rectd_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NE 1 0.4 23349 -4427.7
## - BAL 1 0.5 23349 -4427.7
## - TB 1 0.6 23349 -4427.6
## - hot_weather 1 0.6 23349 -4427.5
## - WAS 1 0.6 23349 -4427.5
## - DET 1 0.8 23349 -4427.3
## - grass_1 1 0.9 23349 -4427.2
## - NYG 1 1.0 23349 -4427.0
## - KC 1 1.0 23349 -4427.0
## - JAC 1 1.1 23349 -4427.0
## - OAK 1 1.1 23349 -4427.0
## - DEN 1 1.1 23349 -4427.0
## - GB 1 1.2 23349 -4426.9
## - TEN 1 1.4 23350 -4426.6
## - CIN 1 1.4 23350 -4426.6
## <none> 23348 -4426.3
## - SD 1 1.8 23350 -4426.1
## - CAR 1 1.8 23350 -4426.1
## - PIT 1 1.8 23350 -4426.1
## - BUF 1 1.9 23350 -4426.0
## - DAL 1 2.0 23350 -4425.9
## - IND 1 2.0 23350 -4425.9
## - home_team_1 1 2.7 23351 -4425.1
## - CHI 1 2.7 23351 -4425.0
## - bad_weather_1 1 3.1 23351 -4424.6
## - ATL 1 3.4 23352 -4424.3
## - NOR 1 6.4 23355 -4420.7
## - avg_rectd_plyr 1 3970.9 27319 -111.5
##
## Step: AIC=-4427.74
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI +
## CIN + DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG +
## OAK + PIT + SD + TB + TEN + WAS + avg_rectd_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BAL 1 0.4 23349 -4429.3
## - TB 1 0.5 23349 -4429.2
## - WAS 1 0.5 23349 -4429.1
## - hot_weather 1 0.6 23349 -4429.0
## - DET 1 0.7 23349 -4428.9
## - NYG 1 0.9 23350 -4428.7
## - KC 1 0.9 23350 -4428.6
## - JAC 1 0.9 23350 -4428.6
## - OAK 1 1.0 23350 -4428.6
## - DEN 1 1.0 23350 -4428.6
## - grass_1 1 1.0 23350 -4428.5
## - GB 1 1.0 23350 -4428.5
## - TEN 1 1.3 23350 -4428.3
## - CIN 1 1.3 23350 -4428.3
## - SD 1 1.7 23350 -4427.8
## - CAR 1 1.7 23350 -4427.8
## - PIT 1 1.7 23350 -4427.8
## <none> 23349 -4427.7
## - BUF 1 1.7 23350 -4427.7
## - DAL 1 1.8 23350 -4427.6
## - IND 1 1.9 23351 -4427.5
## - CHI 1 2.6 23351 -4426.7
## - home_team_1 1 2.9 23352 -4426.4
## - ATL 1 3.2 23352 -4426.0
## - bad_weather_1 1 3.2 23352 -4426.0
## - NOR 1 6.1 23355 -4422.5
## - avg_rectd_plyr 1 4003.8 27352 -80.0
##
## Step: AIC=-4429.27
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG + OAK +
## PIT + SD + TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TB 1 0.4 23349 -4430.8
## - WAS 1 0.5 23350 -4430.7
## - hot_weather 1 0.6 23350 -4430.5
## - DET 1 0.6 23350 -4430.5
## - NYG 1 0.8 23350 -4430.3
## - KC 1 0.8 23350 -4430.3
## - JAC 1 0.9 23350 -4430.3
## - OAK 1 0.9 23350 -4430.3
## - DEN 1 0.9 23350 -4430.2
## - GB 1 0.9 23350 -4430.2
## - grass_1 1 1.1 23350 -4430.0
## - TEN 1 1.1 23350 -4429.9
## - CIN 1 1.1 23350 -4429.9
## - SD 1 1.5 23351 -4429.5
## - CAR 1 1.6 23351 -4429.4
## - PIT 1 1.6 23351 -4429.4
## - BUF 1 1.6 23351 -4429.4
## <none> 23349 -4429.3
## - DAL 1 1.7 23351 -4429.3
## - IND 1 1.7 23351 -4429.2
## - CHI 1 2.4 23351 -4428.4
## - home_team_1 1 3.0 23352 -4427.8
## - ATL 1 3.0 23352 -4427.7
## - bad_weather_1 1 3.2 23352 -4427.6
## - NOR 1 5.9 23355 -4424.3
## - avg_rectd_plyr 1 4003.5 27353 -81.8
##
## Step: AIC=-4430.78
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG + OAK +
## PIT + SD + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - WAS 1 0.4 23350 -4432.3
## - DET 1 0.6 23350 -4432.1
## - hot_weather 1 0.6 23350 -4432.1
## - NYG 1 0.7 23350 -4431.9
## - KC 1 0.8 23350 -4431.9
## - JAC 1 0.8 23350 -4431.9
## - OAK 1 0.8 23350 -4431.9
## - DEN 1 0.8 23350 -4431.9
## - GB 1 0.8 23350 -4431.8
## - grass_1 1 1.0 23350 -4431.7
## - TEN 1 1.0 23350 -4431.6
## - CIN 1 1.1 23351 -4431.5
## - SD 1 1.4 23351 -4431.1
## - CAR 1 1.4 23351 -4431.1
## - PIT 1 1.4 23351 -4431.1
## - BUF 1 1.5 23351 -4431.0
## - DAL 1 1.6 23351 -4430.9
## - IND 1 1.6 23351 -4430.8
## <none> 23349 -4430.8
## - CHI 1 2.3 23352 -4430.1
## - ATL 1 2.9 23352 -4429.4
## - home_team_1 1 3.1 23353 -4429.2
## - bad_weather_1 1 3.1 23353 -4429.1
## - NOR 1 5.7 23355 -4426.1
## - avg_rectd_plyr 1 4003.5 27353 -83.4
##
## Step: AIC=-4432.32
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG + OAK +
## PIT + SD + TEN + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DET 1 0.5 23350 -4433.7
## - hot_weather 1 0.6 23350 -4433.6
## - KC 1 0.7 23351 -4433.5
## - NYG 1 0.7 23351 -4433.5
## - OAK 1 0.7 23351 -4433.5
## - JAC 1 0.7 23351 -4433.5
## - DEN 1 0.7 23351 -4433.5
## - GB 1 0.8 23351 -4433.4
## - grass_1 1 0.8 23351 -4433.3
## - TEN 1 0.9 23351 -4433.2
## - CIN 1 1.0 23351 -4433.2
## - SD 1 1.3 23351 -4432.8
## - CAR 1 1.3 23351 -4432.8
## - PIT 1 1.3 23351 -4432.8
## - BUF 1 1.4 23351 -4432.7
## - DAL 1 1.5 23351 -4432.5
## - IND 1 1.5 23351 -4432.5
## <none> 23350 -4432.3
## - CHI 1 2.1 23352 -4431.8
## - ATL 1 2.7 23353 -4431.1
## - bad_weather_1 1 3.1 23353 -4430.7
## - home_team_1 1 3.1 23353 -4430.6
## - NOR 1 5.5 23355 -4427.8
## - avg_rectd_plyr 1 4003.3 27353 -85.2
##
## Step: AIC=-4433.7
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + GB + IND + JAC + KC + NOR + NYG + OAK + PIT +
## SD + TEN + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NYG 1 0.6 23351 -4435.0
## - KC 1 0.6 23351 -4435.0
## - OAK 1 0.6 23351 -4435.0
## - JAC 1 0.6 23351 -4435.0
## - hot_weather 1 0.6 23351 -4435.0
## - DEN 1 0.6 23351 -4435.0
## - GB 1 0.7 23351 -4434.9
## - TEN 1 0.9 23351 -4434.7
## - CIN 1 0.9 23351 -4434.7
## - grass_1 1 0.9 23351 -4434.6
## - SD 1 1.2 23352 -4434.3
## - CAR 1 1.2 23352 -4434.3
## - PIT 1 1.2 23352 -4434.3
## - BUF 1 1.3 23352 -4434.2
## - DAL 1 1.4 23352 -4434.1
## - IND 1 1.4 23352 -4434.0
## <none> 23350 -4433.7
## - CHI 1 2.0 23352 -4433.3
## - ATL 1 2.6 23353 -4432.7
## - home_team_1 1 3.0 23353 -4432.2
## - bad_weather_1 1 3.1 23353 -4432.1
## - NOR 1 5.3 23356 -4429.5
## - avg_rectd_plyr 1 4013.9 27364 -76.0
##
## Step: AIC=-4435
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + GB + IND + JAC + KC + NOR + OAK + PIT + SD +
## TEN + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - KC 1 0.5 23352 -4436.4
## - OAK 1 0.6 23352 -4436.4
## - JAC 1 0.6 23352 -4436.3
## - DEN 1 0.6 23352 -4436.3
## - GB 1 0.6 23352 -4436.3
## - hot_weather 1 0.6 23352 -4436.3
## - TEN 1 0.8 23352 -4436.1
## - CIN 1 0.8 23352 -4436.1
## - grass_1 1 1.0 23352 -4435.8
## - CAR 1 1.1 23352 -4435.7
## - PIT 1 1.1 23352 -4435.7
## - SD 1 1.1 23352 -4435.7
## - BUF 1 1.2 23352 -4435.6
## - DAL 1 1.3 23352 -4435.5
## - IND 1 1.3 23352 -4435.5
## <none> 23351 -4435.0
## - CHI 1 1.9 23353 -4434.7
## - ATL 1 2.4 23353 -4434.1
## - home_team_1 1 3.1 23354 -4433.4
## - bad_weather_1 1 3.2 23354 -4433.3
## - NOR 1 5.1 23356 -4431.0
## - avg_rectd_plyr 1 4017.9 27369 -73.4
##
## Step: AIC=-4436.36
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + GB + IND + JAC + NOR + OAK + PIT + SD + TEN +
## avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.5 23352 -4437.8
## - JAC 1 0.5 23352 -4437.8
## - DEN 1 0.5 23352 -4437.8
## - GB 1 0.5 23352 -4437.7
## - hot_weather 1 0.7 23352 -4437.6
## - TEN 1 0.7 23352 -4437.5
## - CIN 1 0.7 23352 -4437.5
## - grass_1 1 0.9 23352 -4437.4
## - PIT 1 1.0 23353 -4437.2
## - CAR 1 1.0 23353 -4437.2
## - SD 1 1.0 23353 -4437.2
## - BUF 1 1.1 23353 -4437.1
## - DAL 1 1.2 23353 -4436.9
## - IND 1 1.2 23353 -4436.9
## <none> 23352 -4436.4
## - CHI 1 1.8 23353 -4436.3
## - ATL 1 2.3 23354 -4435.6
## - home_team_1 1 3.1 23355 -4434.7
## - bad_weather_1 1 3.2 23355 -4434.6
## - NOR 1 4.9 23356 -4432.6
## - avg_rectd_plyr 1 4018.8 27370 -73.9
##
## Step: AIC=-4437.81
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + GB + IND + JAC + NOR + PIT + SD + TEN + avg_rectd_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - JAC 1 0.4 23352 -4439.3
## - DEN 1 0.4 23352 -4439.3
## - GB 1 0.5 23352 -4439.3
## - TEN 1 0.6 23353 -4439.1
## - CIN 1 0.7 23353 -4439.0
## - hot_weather 1 0.7 23353 -4439.0
## - grass_1 1 0.7 23353 -4439.0
## - PIT 1 0.9 23353 -4438.7
## - SD 1 0.9 23353 -4438.7
## - CAR 1 0.9 23353 -4438.7
## - BUF 1 1.0 23353 -4438.6
## - DAL 1 1.2 23353 -4438.5
## - IND 1 1.2 23353 -4438.4
## - CHI 1 1.7 23354 -4437.8
## <none> 23352 -4437.8
## - ATL 1 2.2 23354 -4437.2
## - home_team_1 1 3.1 23355 -4436.1
## - bad_weather_1 1 3.2 23355 -4436.1
## - NOR 1 4.8 23357 -4434.2
## - avg_rectd_plyr 1 4018.4 27370 -75.9
##
## Step: AIC=-4439.31
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + DEN + GB + IND + NOR + PIT + SD + TEN + avg_rectd_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DEN 1 0.4 23353 -4440.9
## - GB 1 0.4 23353 -4440.8
## - TEN 1 0.6 23353 -4440.6
## - CIN 1 0.6 23353 -4440.6
## - grass_1 1 0.6 23353 -4440.6
## - hot_weather 1 0.7 23353 -4440.5
## - PIT 1 0.9 23353 -4440.3
## - SD 1 0.9 23353 -4440.3
## - CAR 1 0.9 23353 -4440.3
## - BUF 1 1.0 23353 -4440.1
## - DAL 1 1.1 23354 -4440.0
## - IND 1 1.1 23354 -4440.0
## - CHI 1 1.6 23354 -4439.4
## <none> 23352 -4439.3
## - ATL 1 2.2 23355 -4438.8
## - bad_weather_1 1 3.1 23356 -4437.6
## - home_team_1 1 3.2 23356 -4437.6
## - NOR 1 4.7 23357 -4435.8
## - avg_rectd_plyr 1 4018.0 27370 -77.8
##
## Step: AIC=-4440.87
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + GB + IND + NOR + PIT + SD + TEN + avg_rectd_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - GB 1 0.4 23353 -4442.4
## - TEN 1 0.5 23353 -4442.3
## - grass_1 1 0.6 23353 -4442.2
## - CIN 1 0.6 23353 -4442.2
## - hot_weather 1 0.7 23353 -4442.1
## - PIT 1 0.8 23354 -4441.9
## - SD 1 0.8 23354 -4441.9
## - CAR 1 0.8 23354 -4441.9
## - BUF 1 0.9 23354 -4441.8
## - DAL 1 1.0 23354 -4441.6
## - IND 1 1.1 23354 -4441.6
## - CHI 1 1.5 23354 -4441.1
## <none> 23353 -4440.9
## - ATL 1 2.1 23355 -4440.4
## - bad_weather_1 1 3.1 23356 -4439.3
## - home_team_1 1 3.3 23356 -4439.0
## - NOR 1 4.6 23357 -4437.5
## - avg_rectd_plyr 1 4027.6 27380 -69.9
##
## Step: AIC=-4442.44
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + IND + NOR + PIT + SD + TEN + avg_rectd_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TEN 1 0.5 23354 -4443.9
## - grass_1 1 0.5 23354 -4443.9
## - CIN 1 0.6 23354 -4443.8
## - hot_weather 1 0.7 23354 -4443.6
## - PIT 1 0.7 23354 -4443.6
## - SD 1 0.7 23354 -4443.6
## - CAR 1 0.8 23354 -4443.6
## - BUF 1 0.9 23354 -4443.4
## - DAL 1 1.0 23354 -4443.3
## - IND 1 1.0 23354 -4443.2
## - CHI 1 1.4 23355 -4442.7
## <none> 23353 -4442.4
## - ATL 1 2.0 23355 -4442.1
## - bad_weather_1 1 3.1 23356 -4440.7
## - home_team_1 1 3.3 23356 -4440.6
## - NOR 1 4.5 23358 -4439.2
## - avg_rectd_plyr 1 4060.9 27414 -38.1
##
## Step: AIC=-4443.88
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + IND + NOR + PIT + SD + avg_rectd_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 0.4 23354 -4445.4
## - CIN 1 0.5 23354 -4445.3
## - PIT 1 0.7 23354 -4445.1
## - SD 1 0.7 23354 -4445.1
## - CAR 1 0.7 23354 -4445.1
## - hot_weather 1 0.7 23354 -4445.0
## - BUF 1 0.8 23354 -4444.9
## - DAL 1 1.0 23355 -4444.8
## - IND 1 1.0 23355 -4444.7
## - CHI 1 1.4 23355 -4444.3
## <none> 23354 -4443.9
## - ATL 1 2.0 23356 -4443.6
## - bad_weather_1 1 3.0 23357 -4442.3
## - home_team_1 1 3.3 23357 -4442.0
## - NOR 1 4.4 23358 -4440.7
## - avg_rectd_plyr 1 4060.9 27415 -39.6
##
## Step: AIC=-4445.39
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + IND + NOR + PIT + SD + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SD 1 0.6 23355 -4446.7
## - PIT 1 0.6 23355 -4446.7
## - CIN 1 0.6 23355 -4446.7
## - CAR 1 0.6 23355 -4446.6
## - hot_weather 1 0.8 23355 -4446.5
## - BUF 1 1.0 23355 -4446.2
## - DAL 1 1.1 23355 -4446.2
## - IND 1 1.1 23355 -4446.1
## - CHI 1 1.3 23355 -4445.9
## <none> 23354 -4445.4
## - ATL 1 2.1 23356 -4444.9
## - bad_weather_1 1 3.0 23357 -4443.9
## - home_team_1 1 3.0 23357 -4443.8
## - NOR 1 4.6 23359 -4441.9
## - avg_rectd_plyr 1 4061.6 27416 -40.5
##
## Step: AIC=-4446.69
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + IND + NOR + PIT + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PIT 1 0.5 23355 -4448.0
## - CIN 1 0.6 23355 -4448.0
## - CAR 1 0.6 23355 -4448.0
## - hot_weather 1 0.7 23355 -4447.8
## - BUF 1 0.9 23356 -4447.6
## - DAL 1 1.0 23356 -4447.5
## - IND 1 1.0 23356 -4447.5
## - CHI 1 1.2 23356 -4447.3
## <none> 23355 -4446.7
## - ATL 1 2.0 23357 -4446.3
## - bad_weather_1 1 2.9 23358 -4445.2
## - home_team_1 1 3.1 23358 -4445.1
## - NOR 1 4.5 23359 -4443.4
## - avg_rectd_plyr 1 4065.9 27421 -37.6
##
## Step: AIC=-4448.04
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN +
## DAL + IND + NOR + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CIN 1 0.5 23356 -4449.4
## - CAR 1 0.5 23356 -4449.4
## - hot_weather 1 0.7 23356 -4449.2
## - BUF 1 0.9 23356 -4449.0
## - DAL 1 0.9 23356 -4448.9
## - IND 1 1.0 23356 -4448.9
## - CHI 1 1.1 23356 -4448.7
## <none> 23355 -4448.0
## - ATL 1 1.9 23357 -4447.8
## - bad_weather_1 1 3.0 23358 -4446.5
## - home_team_1 1 3.2 23358 -4446.3
## - NOR 1 4.4 23360 -4444.9
## - avg_rectd_plyr 1 4068.9 27424 -36.0
##
## Step: AIC=-4449.42
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + DAL +
## IND + NOR + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CAR 1 0.5 23356 -4450.8
## - hot_weather 1 0.7 23356 -4450.6
## - BUF 1 0.8 23357 -4450.5
## - DAL 1 0.9 23357 -4450.4
## - IND 1 0.9 23357 -4450.3
## - CHI 1 1.1 23357 -4450.1
## <none> 23356 -4449.4
## - ATL 1 1.9 23358 -4449.2
## - bad_weather_1 1 3.0 23359 -4447.8
## - home_team_1 1 3.2 23359 -4447.6
## - NOR 1 4.3 23360 -4446.4
## - avg_rectd_plyr 1 4068.4 27424 -38.0
##
## Step: AIC=-4450.84
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CHI + DAL + IND +
## NOR + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.7 23357 -4452.0
## - BUF 1 0.8 23357 -4451.9
## - DAL 1 0.8 23357 -4451.8
## - IND 1 0.9 23357 -4451.8
## - CHI 1 1.0 23357 -4451.6
## <none> 23356 -4450.8
## - ATL 1 1.8 23358 -4450.7
## - bad_weather_1 1 3.0 23359 -4449.3
## - home_team_1 1 3.3 23359 -4449.0
## - NOR 1 4.2 23360 -4447.9
## - avg_rectd_plyr 1 4067.9 27424 -40.0
##
## Step: AIC=-4451.97
## tdrec ~ home_team_1 + ATL + BUF + CHI + DAL + IND + NOR + avg_rectd_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.7 23358 -4453.1
## - DAL 1 0.9 23358 -4453.0
## - IND 1 0.9 23358 -4452.9
## - CHI 1 1.0 23358 -4452.7
## <none> 23357 -4452.0
## - ATL 1 1.8 23359 -4451.8
## - bad_weather_1 1 3.1 23360 -4450.3
## - home_team_1 1 3.3 23360 -4450.1
## - NOR 1 4.1 23361 -4449.1
## - avg_rectd_plyr 1 4067.6 27425 -41.5
##
## Step: AIC=-4453.11
## tdrec ~ home_team_1 + ATL + CHI + DAL + IND + NOR + avg_rectd_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DAL 1 0.8 23358 -4454.2
## - IND 1 0.8 23359 -4454.1
## - CHI 1 1.0 23359 -4453.9
## <none> 23358 -4453.1
## - ATL 1 1.7 23359 -4453.1
## - bad_weather_1 1 3.1 23361 -4451.4
## - home_team_1 1 3.3 23361 -4451.2
## - NOR 1 4.0 23362 -4450.4
## - avg_rectd_plyr 1 4067.0 27425 -43.5
##
## Step: AIC=-4454.15
## tdrec ~ home_team_1 + ATL + CHI + IND + NOR + avg_rectd_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - IND 1 0.8 23359 -4455.3
## - CHI 1 0.9 23359 -4455.1
## - ATL 1 1.6 23360 -4454.3
## <none> 23358 -4454.2
## - home_team_1 1 2.9 23361 -4452.7
## - bad_weather_1 1 3.1 23362 -4452.5
## - NOR 1 3.8 23362 -4451.7
## - avg_rectd_plyr 1 4077.6 27436 -34.0
##
## Step: AIC=-4455.27
## tdrec ~ home_team_1 + ATL + CHI + NOR + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CHI 1 0.9 23360 -4456.2
## - ATL 1 1.5 23361 -4455.5
## <none> 23359 -4455.3
## - home_team_1 1 2.6 23362 -4454.2
## - bad_weather_1 1 3.1 23362 -4453.6
## - NOR 1 3.7 23363 -4452.9
## - avg_rectd_plyr 1 4080.3 27439 -32.6
##
## Step: AIC=-4456.23
## tdrec ~ home_team_1 + ATL + NOR + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ATL 1 1.4 23362 -4456.5
## <none> 23360 -4456.2
## - home_team_1 1 2.7 23363 -4455.0
## - bad_weather_1 1 3.2 23363 -4454.4
## - NOR 1 3.6 23364 -4454.0
## - avg_rectd_plyr 1 4079.7 27440 -34.3
##
## Step: AIC=-4456.53
## tdrec ~ home_team_1 + NOR + avg_rectd_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## <none> 23362 -4456.5
## - home_team_1 1 2.3 23364 -4455.9
## - bad_weather_1 1 3.1 23365 -4454.8
## - NOR 1 3.4 23365 -4454.6
## - avg_rectd_plyr 1 4087.2 27449 -27.3Passing
Passing Yards
PreProcess:
set.seed(123)
splitpy <- sample.split(nfl_data$py, SplitRatio = 0.7)
Trainpy <- subset(nfl_data, split == TRUE)
Testpy <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainpy, method = c("center", "scale"))
trainTransformedpy <- predict(preProcValues, Trainpy)
testTransformedpy <- predict(preProcValues, Testpy)ggpairs:
ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[46:51]))])
Regression:
pyregform <- formula(paste("py ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegQBpyds <- lm(pyregform, data = trainTransformedpy)
summary(linRegQBpyds)##
## Call:
## lm(formula = pyregform, data = trainTransformedpy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0235 -0.0522 -0.0126 0.0295 4.9218
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.296e-15 2.338e-03 0.000 1.000000
## height 4.426e-02 4.537e-03 9.756 < 2e-16 ***
## weight -2.624e-02 4.252e-03 -6.170 6.93e-10 ***
## cold_weather -7.137e-03 2.462e-03 -2.900 0.003740 **
## hot_weather -2.222e-03 2.360e-03 -0.941 0.346472
## home_team_1 2.547e-03 2.544e-03 1.001 0.316727
## forty1 1.476e-02 4.036e-03 3.657 0.000256 ***
## vertical1 -1.170e-02 3.103e-03 -3.772 0.000162 ***
## ARI -6.302e-04 3.271e-03 -0.193 0.847232
## ATL -5.329e-03 3.287e-03 -1.621 0.104973
## BAL -2.789e-03 3.290e-03 -0.848 0.396465
## BUF -2.859e-04 3.247e-03 -0.088 0.929834
## CAR -6.943e-04 3.226e-03 -0.215 0.829610
## CHI -5.189e-03 3.190e-03 -1.627 0.103848
## CIN -7.107e-03 3.249e-03 -2.187 0.028718 *
## CLE 4.537e-03 3.234e-03 1.403 0.160610
## DAL -1.184e-02 3.267e-03 -3.623 0.000291 ***
## DEN -5.007e-03 3.279e-03 -1.527 0.126763
## DET -3.076e-03 3.234e-03 -0.951 0.341491
## GB -1.887e-02 3.329e-03 -5.668 1.46e-08 ***
## HOU 5.940e-03 3.290e-03 1.806 0.070961 .
## IND -6.637e-03 3.266e-03 -2.032 0.042118 *
## JAC -2.851e-03 3.186e-03 -0.895 0.370848
## KC 2.147e-03 3.255e-03 0.660 0.509512
## MIA -2.479e-03 3.203e-03 -0.774 0.438955
## MINN 1.991e-03 3.223e-03 0.618 0.536695
## NE -1.560e-02 3.366e-03 -4.637 3.56e-06 ***
## NOR -1.218e-02 3.355e-03 -3.631 0.000283 ***
## NYG -9.752e-03 3.279e-03 -2.974 0.002946 **
## NYJ -4.306e-03 3.267e-03 -1.318 0.187529
## OAK -4.814e-03 3.288e-03 -1.464 0.143206
## PHI 5.844e-03 3.186e-03 1.834 0.066651 .
## PIT -1.521e-03 3.270e-03 -0.465 0.641843
## SD -1.145e-02 3.209e-03 -3.567 0.000361 ***
## SEA -4.269e-04 3.330e-03 -0.128 0.897991
## STL -1.781e-03 3.241e-03 -0.550 0.582613
## TB -6.106e-03 3.211e-03 -1.902 0.057206 .
## TEN -3.634e-03 3.230e-03 -1.125 0.260596
## WAS 5.401e-03 3.247e-03 1.663 0.096247 .
## avg_trg_team NA NA NA NA
## avg_rectd_plyr -1.591e-02 2.986e-03 -5.326 1.01e-07 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr -2.445e-02 3.574e-03 -6.841 8.04e-12 ***
## avg_rbry_pos 1.339e-02 4.164e-03 3.216 0.001300 **
## avg_fuml_plyr 7.685e-02 3.454e-03 22.249 < 2e-16 ***
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr 8.464e-01 3.752e-03 225.574 < 2e-16 ***
## avg_qbtdp_team NA NA NA NA
## grass_1 -2.140e-03 2.690e-03 -0.795 0.426406
## bad_weather_1 -5.485e-03 2.379e-03 -2.306 0.021139 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3877 on 27438 degrees of freedom
## Multiple R-squared: 0.85, Adjusted R-squared: 0.8497
## F-statistic: 3454 on 45 and 27438 DF, p-value: < 2.2e-16linRegQBpyds2 <- update(linRegQBpyds, ~.-hot_weather-home_team_1-vertical1-ATL-BAL-DAL-DEN-DET-KC
-NOR-PHI-PIT-SEA-SD-WAS-avg_trg_team-avg_tdr_team-avg_rbra_team-avg_rbry_plyr
-avg_fuml_team-avg_qbints_team-avg_qbtdp_team-grass_1)
summary(linRegQBpyds2)##
## Call:
## lm(formula = py ~ height + weight + cold_weather + forty1 + ARI +
## BUF + CAR + CHI + CIN + CLE + GB + HOU + IND + JAC + MIA +
## MINN + NE + NYG + NYJ + OAK + STL + TB + TEN + avg_rectd_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1,
## data = trainTransformedpy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0413 -0.0521 -0.0106 0.0261 4.9606
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.289e-15 2.344e-03 0.000 1.000000
## height 4.148e-02 4.525e-03 9.166 < 2e-16 ***
## weight -2.680e-02 4.230e-03 -6.336 2.40e-10 ***
## cold_weather -5.096e-03 2.412e-03 -2.113 0.034614 *
## forty1 2.488e-02 3.391e-03 7.338 2.23e-13 ***
## ARI 3.054e-03 2.400e-03 1.273 0.203163
## BUF 3.269e-03 2.400e-03 1.362 0.173119
## CAR 1.795e-03 2.397e-03 0.749 0.453945
## CHI -2.204e-03 2.401e-03 -0.918 0.358631
## CIN -4.019e-03 2.399e-03 -1.675 0.093918 .
## CLE 7.153e-03 2.410e-03 2.968 0.003001 **
## GB -1.565e-02 2.416e-03 -6.477 9.52e-11 ***
## HOU 8.488e-03 2.408e-03 3.525 0.000424 ***
## IND -3.844e-03 2.395e-03 -1.605 0.108539
## JAC -4.243e-04 2.395e-03 -0.177 0.859370
## MIA 1.151e-03 2.393e-03 0.481 0.630424
## MINN 4.273e-03 2.405e-03 1.777 0.075588 .
## NE -1.233e-02 2.445e-03 -5.044 4.58e-07 ***
## NYG -6.020e-03 2.400e-03 -2.508 0.012151 *
## NYJ -1.940e-03 2.399e-03 -0.809 0.418794
## OAK -9.088e-04 2.413e-03 -0.377 0.706470
## STL 1.559e-03 2.404e-03 0.648 0.516748
## TB -2.803e-03 2.398e-03 -1.169 0.242444
## TEN -7.200e-04 2.401e-03 -0.300 0.764233
## avg_rectd_plyr -1.931e-02 2.963e-03 -6.518 7.25e-11 ***
## avg_rbry_pos -4.247e-03 3.477e-03 -1.221 0.221986
## avg_fuml_plyr 7.115e-02 3.245e-03 21.926 < 2e-16 ***
## avg_qbtdp_plyr 8.484e-01 3.706e-03 228.891 < 2e-16 ***
## bad_weather_1 -5.277e-03 2.379e-03 -2.218 0.026589 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3885 on 27455 degrees of freedom
## Multiple R-squared: 0.8492, Adjusted R-squared: 0.849
## F-statistic: 5521 on 28 and 27455 DF, p-value: < 2.2e-16This prediction actually turned out to be pretty strong (R2 0.87) and we did it with only 5 variables! This makes sense to me. QB is a 1 player position, with a significant investment in the player. A QB will get time to mature and prove himself good or bad.
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
PydsdPredicted <- predict(linRegQBpyds2, newdata = testTransformedpy)
SSEpyds <- sum((PydsdPredicted - testTransformedpy$py)^2)
SSTpyds <- sum((mean(nfl_data$py)-testTransformedpy$py)^2)
r2_pyds <- 1 - SSEpyds/SSTpyds
r2_pyds## [1] 0.999716rmse_pyds <- sqrt(SSEpyds/nrow(testTransformedpy))
rmse_pyds## [1] 0.4007825Below are the regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBpyds2, which = c(1:3,5))
The normal Q-Q shows are data has extreme values, and means the data is probably not normally distributed
Some more summary statistics:
confint(linRegQBpyds2)## 2.5 % 97.5 %
## (Intercept) -0.0045936970 0.0045936970
## height 0.0326078543 0.0503464791
## weight -0.0350933025 -0.0185105021
## cold_weather -0.0098236426 -0.0003687761
## forty1 0.0182347552 0.0315260322
## ARI -0.0016498965 0.0077587289
## BUF -0.0014345387 0.0079730819
## CAR -0.0029037966 0.0064945761
## CHI -0.0069102798 0.0025020177
## CIN -0.0087219695 0.0006835929
## CLE 0.0024291162 0.0118777163
## GB -0.0203876978 -0.0109148362
## HOU 0.0037682390 0.0132071276
## IND -0.0085392589 0.0008508465
## JAC -0.0051186886 0.0042700044
## MIA -0.0035383674 0.0058406447
## MINN -0.0004402949 0.0089861675
## NE -0.0171234530 -0.0075402464
## NYG -0.0107246243 -0.0013150442
## NYJ -0.0066413585 0.0027623132
## OAK -0.0056389235 0.0038212445
## STL -0.0031534987 0.0062711114
## TB -0.0075025120 0.0018969260
## TEN -0.0054253315 0.0039853018
## avg_rectd_plyr -0.0251213934 -0.0135056939
## avg_rbry_pos -0.0110621988 0.0025688193
## avg_fuml_plyr 0.0647915244 0.0775128589
## avg_qbtdp_plyr 0.8410944287 0.8556238723
## bad_weather_1 -0.0099402225 -0.0006128489coef(summary(linRegQBpyds2))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.288901e-15 0.002343663 5.499515e-13 1.000000e+00
## height 4.147717e-02 0.004525043 9.166137e+00 5.235466e-20
## weight -2.680190e-02 0.004230197 -6.335851e+00 2.396931e-10
## cold_weather -5.096209e-03 0.002411894 -2.112949e+00 3.461410e-02
## forty1 2.488039e-02 0.003390545 7.338170e+00 2.225360e-13
## ARI 3.054416e-03 0.002400098 1.272622e+00 2.031631e-01
## BUF 3.269272e-03 0.002399842 1.362286e+00 1.731187e-01
## CAR 1.795390e-03 0.002397482 7.488646e-01 4.539452e-01
## CHI -2.204131e-03 0.002401035 -9.179922e-01 3.586310e-01
## CIN -4.019188e-03 0.002399316 -1.675139e+00 9.391838e-02
## CLE 7.153416e-03 0.002410295 2.967859e+00 3.001405e-03
## GB -1.565127e-02 0.002416484 -6.476875e+00 9.522448e-11
## HOU 8.487683e-03 0.002407818 3.525052e+00 4.240887e-04
## IND -3.844206e-03 0.002395373 -1.604846e+00 1.085391e-01
## JAC -4.243421e-04 0.002395013 -1.771774e-01 8.593704e-01
## MIA 1.151139e-03 0.002392544 4.811359e-01 6.304237e-01
## MINN 4.272936e-03 0.002404648 1.776949e+00 7.558773e-02
## NE -1.233185e-02 0.002444633 -5.044459e+00 4.577027e-07
## NYG -6.019834e-03 0.002400341 -2.507908e+00 1.215057e-02
## NYJ -1.939523e-03 0.002398834 -8.085272e-01 4.187942e-01
## OAK -9.088395e-04 0.002413246 -3.766046e-01 7.064704e-01
## STL 1.558806e-03 0.002404175 6.483746e-01 5.167481e-01
## TB -2.802793e-03 0.002397754 -1.168924e+00 2.424443e-01
## TEN -7.200148e-04 0.002400610 -2.999299e-01 7.642329e-01
## avg_rectd_plyr -1.931354e-02 0.002963112 -6.517992e+00 7.248974e-11
## avg_rbry_pos -4.246690e-03 0.003477211 -1.221292e+00 2.219860e-01
## avg_fuml_plyr 7.115219e-02 0.003245155 2.192567e+01 1.193963e-105
## avg_qbtdp_plyr 8.483592e-01 0.003706395 2.288906e+02 0.000000e+00
## bad_weather_1 -5.276536e-03 0.002379371 -2.217618e+00 2.658904e-02anova(linRegQBpyds2)## Analysis of Variance Table
##
## Response: py
## Df Sum Sq Mean Sq F value Pr(>F)
## height 1 1859.7 1859.7 12318.8750 < 2.2e-16 ***
## weight 1 446.2 446.2 2955.3921 < 2.2e-16 ***
## cold_weather 1 0.7 0.7 4.3623 0.0367522 *
## forty1 1 5442.0 5442.0 36048.5596 < 2.2e-16 ***
## ARI 1 0.4 0.4 2.8024 0.0941360 .
## BUF 1 0.5 0.5 3.6101 0.0574397 .
## CAR 1 10.9 10.9 71.9797 < 2.2e-16 ***
## CHI 1 0.1 0.1 0.6070 0.4359401
## CIN 1 4.2 4.2 27.8127 1.347e-07 ***
## CLE 1 1.9 1.9 12.7879 0.0003495 ***
## GB 1 0.0 0.0 0.0314 0.8593892
## HOU 1 15.1 15.1 100.2842 < 2.2e-16 ***
## IND 1 11.3 11.3 74.6888 < 2.2e-16 ***
## JAC 1 0.0 0.0 0.0713 0.7895004
## MIA 1 0.6 0.6 3.8769 0.0489650 *
## MINN 1 1.9 1.9 12.5342 0.0004002 ***
## NE 1 34.2 34.2 226.3528 < 2.2e-16 ***
## NYG 1 7.3 7.3 48.0341 4.281e-12 ***
## NYJ 1 0.8 0.8 5.1984 0.0226151 *
## OAK 1 0.1 0.1 0.9377 0.3328731
## STL 1 26.8 26.8 177.4989 < 2.2e-16 ***
## TB 1 3.2 3.2 20.8947 4.874e-06 ***
## TEN 1 5.7 5.7 38.0459 7.006e-10 ***
## avg_rectd_plyr 1 1872.3 1872.3 12402.0890 < 2.2e-16 ***
## avg_rbry_pos 1 311.0 311.0 2060.3374 < 2.2e-16 ***
## avg_fuml_plyr 1 5371.6 5371.6 35582.4880 < 2.2e-16 ***
## avg_qbtdp_plyr 1 7909.1 7909.1 52391.3106 < 2.2e-16 ***
## bad_weather_1 1 0.7 0.7 4.9178 0.0265890 *
## Residuals 27455 4144.7 0.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_py <- step(lm(pyregform, data = trainTransformedpy), direction = "backward")## Start: AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.0 4123.6 -52044
## - SEA 1 0.0 4123.6 -52044
## - ARI 1 0.0 4123.6 -52044
## - CAR 1 0.0 4123.6 -52044
## - PIT 1 0.0 4123.6 -52044
## - STL 1 0.0 4123.6 -52043
## - MINN 1 0.1 4123.7 -52043
## - KC 1 0.1 4123.7 -52043
## - MIA 1 0.1 4123.7 -52043
## - grass_1 1 0.1 4123.7 -52043
## - BAL 1 0.1 4123.7 -52043
## - JAC 1 0.1 4123.7 -52043
## - hot_weather 1 0.1 4123.7 -52043
## - DET 1 0.1 4123.7 -52043
## - home_team_1 1 0.2 4123.8 -52043
## - TEN 1 0.2 4123.8 -52042
## - NYJ 1 0.3 4123.9 -52042
## - CLE 1 0.3 4123.9 -52042
## <none> 4123.6 -52042
## - OAK 1 0.3 4123.9 -52042
## - DEN 1 0.4 4124.0 -52041
## - ATL 1 0.4 4124.0 -52041
## - CHI 1 0.4 4124.0 -52041
## - WAS 1 0.4 4124.0 -52041
## - HOU 1 0.5 4124.1 -52040
## - PHI 1 0.5 4124.1 -52040
## - TB 1 0.5 4124.1 -52040
## - IND 1 0.6 4124.2 -52040
## - CIN 1 0.7 4124.3 -52039
## - bad_weather_1 1 0.8 4124.4 -52038
## - cold_weather 1 1.3 4124.9 -52035
## - NYG 1 1.3 4124.9 -52035
## - avg_rbry_pos 1 1.6 4125.2 -52033
## - SD 1 1.9 4125.5 -52031
## - DAL 1 2.0 4125.6 -52031
## - NOR 1 2.0 4125.6 -52031
## - forty1 1 2.0 4125.6 -52030
## - vertical1 1 2.1 4125.7 -52030
## - NE 1 3.2 4126.8 -52022
## - avg_rectd_plyr 1 4.3 4127.9 -52015
## - GB 1 4.8 4128.4 -52012
## - weight 1 5.7 4129.3 -52006
## - avg_rbry_plyr 1 7.0 4130.6 -51997
## - height 1 14.3 4137.9 -51949
## - avg_fuml_plyr 1 74.4 4198.0 -51552
## - avg_qbtdp_plyr 1 7647.2 11770.8 -23216
##
## Step: AIC=-52043.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + CAR + CHI + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.0 4123.6 -52046
## - ARI 1 0.0 4123.6 -52046
## - CAR 1 0.0 4123.6 -52046
## - PIT 1 0.0 4123.6 -52046
## - STL 1 0.1 4123.7 -52045
## - MINN 1 0.1 4123.7 -52045
## - grass_1 1 0.1 4123.7 -52045
## - KC 1 0.1 4123.7 -52045
## - MIA 1 0.1 4123.7 -52045
## - BAL 1 0.1 4123.7 -52045
## - hot_weather 1 0.1 4123.7 -52045
## - JAC 1 0.1 4123.7 -52045
## - home_team_1 1 0.2 4123.8 -52045
## - DET 1 0.2 4123.8 -52045
## - TEN 1 0.2 4123.8 -52044
## <none> 4123.6 -52044
## - NYJ 1 0.3 4123.9 -52044
## - OAK 1 0.4 4124.0 -52043
## - CLE 1 0.4 4124.0 -52043
## - DEN 1 0.4 4124.0 -52043
## - CHI 1 0.5 4124.1 -52042
## - ATL 1 0.5 4124.1 -52042
## - WAS 1 0.6 4124.2 -52042
## - TB 1 0.7 4124.3 -52041
## - HOU 1 0.7 4124.3 -52041
## - PHI 1 0.7 4124.3 -52041
## - IND 1 0.8 4124.4 -52041
## - bad_weather_1 1 0.8 4124.4 -52040
## - CIN 1 0.9 4124.5 -52040
## - cold_weather 1 1.3 4124.9 -52037
## - avg_rbry_pos 1 1.6 4125.2 -52035
## - NYG 1 1.7 4125.3 -52034
## - forty1 1 2.0 4125.6 -52032
## - vertical1 1 2.1 4125.7 -52031
## - SD 1 2.4 4126.0 -52030
## - DAL 1 2.5 4126.1 -52029
## - NOR 1 2.6 4126.2 -52028
## - NE 1 4.2 4127.8 -52018
## - avg_rectd_plyr 1 4.3 4127.9 -52017
## - weight 1 5.7 4129.3 -52008
## - GB 1 6.3 4129.9 -52004
## - avg_rbry_plyr 1 7.0 4130.6 -51999
## - height 1 14.3 4137.9 -51950
## - avg_fuml_plyr 1 74.4 4198.0 -51554
## - avg_qbtdp_plyr 1 7651.6 11775.2 -23208
##
## Step: AIC=-52045.74
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + CAR + CHI + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ARI 1 0.0 4123.6 -52048
## - CAR 1 0.0 4123.6 -52048
## - PIT 1 0.0 4123.6 -52048
## - STL 1 0.1 4123.7 -52047
## - grass_1 1 0.1 4123.7 -52047
## - MINN 1 0.1 4123.7 -52047
## - MIA 1 0.1 4123.7 -52047
## - KC 1 0.1 4123.7 -52047
## - hot_weather 1 0.1 4123.7 -52047
## - BAL 1 0.1 4123.7 -52047
## - JAC 1 0.1 4123.8 -52047
## - home_team_1 1 0.2 4123.8 -52047
## - DET 1 0.2 4123.8 -52047
## - TEN 1 0.2 4123.8 -52046
## <none> 4123.6 -52046
## - NYJ 1 0.4 4124.0 -52045
## - OAK 1 0.4 4124.0 -52045
## - DEN 1 0.5 4124.1 -52045
## - CLE 1 0.5 4124.1 -52045
## - CHI 1 0.5 4124.1 -52044
## - ATL 1 0.5 4124.1 -52044
## - WAS 1 0.7 4124.3 -52043
## - TB 1 0.7 4124.3 -52043
## - PHI 1 0.8 4124.4 -52042
## - HOU 1 0.8 4124.4 -52042
## - bad_weather_1 1 0.8 4124.4 -52042
## - IND 1 0.9 4124.5 -52042
## - CIN 1 1.0 4124.6 -52041
## - cold_weather 1 1.3 4124.9 -52039
## - avg_rbry_pos 1 1.6 4125.2 -52037
## - NYG 1 1.9 4125.5 -52035
## - forty1 1 2.0 4125.6 -52034
## - vertical1 1 2.1 4125.7 -52033
## - SD 1 2.6 4126.2 -52030
## - DAL 1 2.8 4126.4 -52029
## - NOR 1 2.9 4126.5 -52028
## - avg_rectd_plyr 1 4.3 4127.9 -52019
## - NE 1 4.8 4128.4 -52016
## - weight 1 5.7 4129.3 -52010
## - avg_rbry_plyr 1 7.0 4130.6 -52001
## - GB 1 7.1 4130.7 -52001
## - height 1 14.4 4138.0 -51952
## - avg_fuml_plyr 1 74.6 4198.2 -51555
## - avg_qbtdp_plyr 1 7668.9 11792.5 -23169
##
## Step: AIC=-52047.72
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + BAL + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CAR 1 0.0 4123.6 -52050
## - PIT 1 0.0 4123.6 -52050
## - STL 1 0.0 4123.7 -52049
## - grass_1 1 0.1 4123.7 -52049
## - MIA 1 0.1 4123.7 -52049
## - MINN 1 0.1 4123.7 -52049
## - hot_weather 1 0.1 4123.7 -52049
## - KC 1 0.1 4123.7 -52049
## - BAL 1 0.1 4123.7 -52049
## - JAC 1 0.1 4123.8 -52049
## - home_team_1 1 0.2 4123.8 -52049
## - DET 1 0.2 4123.8 -52049
## - TEN 1 0.2 4123.9 -52048
## <none> 4123.6 -52048
## - NYJ 1 0.4 4124.0 -52047
## - OAK 1 0.4 4124.0 -52047
## - DEN 1 0.5 4124.1 -52047
## - CLE 1 0.5 4124.1 -52046
## - CHI 1 0.5 4124.1 -52046
## - ATL 1 0.5 4124.2 -52046
## - WAS 1 0.7 4124.3 -52045
## - TB 1 0.8 4124.4 -52045
## - bad_weather_1 1 0.8 4124.4 -52044
## - PHI 1 0.9 4124.5 -52044
## - HOU 1 0.9 4124.5 -52044
## - IND 1 0.9 4124.5 -52044
## - CIN 1 1.0 4124.7 -52043
## - cold_weather 1 1.3 4124.9 -52041
## - avg_rbry_pos 1 1.6 4125.2 -52039
## - NYG 1 2.0 4125.6 -52036
## - forty1 1 2.0 4125.6 -52036
## - vertical1 1 2.1 4125.7 -52035
## - SD 1 2.7 4126.4 -52031
## - DAL 1 3.0 4126.6 -52030
## - NOR 1 3.1 4126.7 -52029
## - avg_rectd_plyr 1 4.3 4127.9 -52021
## - NE 1 5.0 4128.6 -52017
## - weight 1 5.7 4129.3 -52012
## - avg_rbry_plyr 1 7.0 4130.7 -52003
## - GB 1 7.4 4131.0 -52000
## - height 1 14.4 4138.0 -51954
## - avg_fuml_plyr 1 74.6 4198.2 -51557
## - avg_qbtdp_plyr 1 7675.3 11798.9 -23156
##
## Step: AIC=-52049.69
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PIT 1 0.0 4123.6 -52052
## - STL 1 0.0 4123.7 -52051
## - grass_1 1 0.1 4123.7 -52051
## - MIA 1 0.1 4123.7 -52051
## - BAL 1 0.1 4123.7 -52051
## - hot_weather 1 0.1 4123.7 -52051
## - MINN 1 0.1 4123.7 -52051
## - JAC 1 0.1 4123.8 -52051
## - KC 1 0.2 4123.8 -52051
## - home_team_1 1 0.2 4123.8 -52051
## - DET 1 0.2 4123.8 -52051
## - TEN 1 0.2 4123.9 -52050
## <none> 4123.6 -52050
## - NYJ 1 0.4 4124.0 -52049
## - OAK 1 0.4 4124.1 -52049
## - DEN 1 0.5 4124.1 -52048
## - CHI 1 0.5 4124.2 -52048
## - ATL 1 0.6 4124.2 -52048
## - CLE 1 0.6 4124.2 -52048
## - TB 1 0.8 4124.4 -52047
## - WAS 1 0.8 4124.4 -52046
## - bad_weather_1 1 0.8 4124.4 -52046
## - IND 1 0.9 4124.5 -52046
## - PHI 1 0.9 4124.5 -52046
## - HOU 1 0.9 4124.5 -52046
## - CIN 1 1.1 4124.7 -52045
## - cold_weather 1 1.3 4124.9 -52043
## - avg_rbry_pos 1 1.6 4125.2 -52041
## - forty1 1 2.0 4125.6 -52038
## - NYG 1 2.0 4125.6 -52038
## - vertical1 1 2.1 4125.8 -52037
## - SD 1 2.8 4126.4 -52033
## - DAL 1 3.0 4126.6 -52032
## - NOR 1 3.2 4126.8 -52031
## - avg_rectd_plyr 1 4.3 4127.9 -52023
## - NE 1 5.1 4128.7 -52018
## - weight 1 5.7 4129.4 -52013
## - avg_rbry_plyr 1 7.0 4130.7 -52005
## - GB 1 7.7 4131.3 -52000
## - height 1 14.4 4138.0 -51956
## - avg_fuml_plyr 1 74.6 4198.2 -51559
## - avg_qbtdp_plyr 1 7675.6 11799.2 -23158
##
## Step: AIC=-52051.5
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + SD + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - STL 1 0.0 4123.7 -52053
## - MIA 1 0.1 4123.7 -52053
## - grass_1 1 0.1 4123.8 -52053
## - BAL 1 0.1 4123.8 -52053
## - JAC 1 0.1 4123.8 -52053
## - hot_weather 1 0.1 4123.8 -52053
## - DET 1 0.2 4123.8 -52053
## - home_team_1 1 0.2 4123.8 -52052
## - MINN 1 0.2 4123.8 -52052
## - KC 1 0.2 4123.8 -52052
## - TEN 1 0.2 4123.9 -52052
## <none> 4123.6 -52052
## - NYJ 1 0.3 4124.0 -52051
## - OAK 1 0.4 4124.1 -52051
## - DEN 1 0.5 4124.1 -52050
## - CHI 1 0.5 4124.2 -52050
## - ATL 1 0.5 4124.2 -52050
## - CLE 1 0.6 4124.3 -52049
## - TB 1 0.7 4124.4 -52049
## - bad_weather_1 1 0.8 4124.4 -52048
## - WAS 1 0.9 4124.5 -52048
## - IND 1 0.9 4124.5 -52048
## - HOU 1 1.0 4124.6 -52047
## - PHI 1 1.0 4124.6 -52047
## - CIN 1 1.0 4124.7 -52047
## - cold_weather 1 1.3 4125.0 -52045
## - avg_rbry_pos 1 1.6 4125.2 -52043
## - forty1 1 2.0 4125.7 -52040
## - NYG 1 2.0 4125.7 -52040
## - vertical1 1 2.1 4125.8 -52039
## - SD 1 2.8 4126.5 -52035
## - DAL 1 3.0 4126.7 -52033
## - NOR 1 3.1 4126.8 -52033
## - avg_rectd_plyr 1 4.3 4127.9 -52025
## - NE 1 5.1 4128.8 -52019
## - weight 1 5.7 4129.4 -52015
## - avg_rbry_plyr 1 7.0 4130.7 -52007
## - GB 1 7.8 4131.5 -52001
## - height 1 14.4 4138.0 -51958
## - avg_fuml_plyr 1 74.6 4198.2 -51561
## - avg_qbtdp_plyr 1 7676.5 11800.1 -23158
##
## Step: AIC=-52053.27
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.1 4123.8 -52055
## - BAL 1 0.1 4123.8 -52055
## - grass_1 1 0.1 4123.8 -52055
## - JAC 1 0.1 4123.8 -52055
## - DET 1 0.1 4123.8 -52054
## - hot_weather 1 0.1 4123.8 -52054
## - home_team_1 1 0.2 4123.8 -52054
## - MINN 1 0.2 4123.9 -52054
## - TEN 1 0.2 4123.9 -52054
## - KC 1 0.2 4123.9 -52054
## <none> 4123.7 -52053
## - NYJ 1 0.3 4124.0 -52053
## - OAK 1 0.4 4124.1 -52053
## - DEN 1 0.4 4124.1 -52052
## - CHI 1 0.5 4124.2 -52052
## - ATL 1 0.5 4124.2 -52052
## - CLE 1 0.7 4124.4 -52051
## - TB 1 0.7 4124.4 -52051
## - bad_weather_1 1 0.8 4124.5 -52050
## - IND 1 0.8 4124.5 -52050
## - WAS 1 0.9 4124.6 -52049
## - CIN 1 1.0 4124.7 -52049
## - PHI 1 1.1 4124.7 -52048
## - HOU 1 1.1 4124.8 -52048
## - cold_weather 1 1.3 4125.0 -52047
## - avg_rbry_pos 1 1.6 4125.2 -52045
## - NYG 1 2.0 4125.7 -52042
## - forty1 1 2.0 4125.7 -52042
## - vertical1 1 2.1 4125.8 -52041
## - SD 1 2.8 4126.5 -52037
## - DAL 1 3.0 4126.7 -52035
## - NOR 1 3.1 4126.8 -52035
## - avg_rectd_plyr 1 4.3 4127.9 -52027
## - NE 1 5.1 4128.8 -52021
## - weight 1 5.7 4129.4 -52017
## - avg_rbry_plyr 1 7.0 4130.7 -52009
## - GB 1 7.8 4131.5 -52003
## - height 1 14.4 4138.0 -51960
## - avg_fuml_plyr 1 74.5 4198.2 -51563
## - avg_qbtdp_plyr 1 7700.6 11824.3 -23103
##
## Step: AIC=-52054.77
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + KC + MINN + NE + NOR +
## NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BAL 1 0.1 4123.8 -52056
## - JAC 1 0.1 4123.8 -52056
## - DET 1 0.1 4123.9 -52056
## - grass_1 1 0.1 4123.9 -52056
## - hot_weather 1 0.1 4123.9 -52056
## - home_team_1 1 0.2 4123.9 -52056
## - TEN 1 0.2 4123.9 -52056
## - MINN 1 0.2 4124.0 -52055
## - KC 1 0.2 4124.0 -52055
## - NYJ 1 0.3 4124.0 -52055
## <none> 4123.8 -52055
## - OAK 1 0.4 4124.1 -52054
## - DEN 1 0.4 4124.1 -52054
## - CHI 1 0.4 4124.2 -52054
## - ATL 1 0.5 4124.2 -52054
## - TB 1 0.7 4124.4 -52052
## - CLE 1 0.8 4124.5 -52052
## - bad_weather_1 1 0.8 4124.5 -52052
## - IND 1 0.8 4124.6 -52051
## - CIN 1 0.9 4124.7 -52050
## - WAS 1 1.0 4124.8 -52050
## - PHI 1 1.2 4124.9 -52049
## - HOU 1 1.2 4124.9 -52049
## - cold_weather 1 1.3 4125.0 -52048
## - avg_rbry_pos 1 1.5 4125.3 -52047
## - NYG 1 1.9 4125.7 -52044
## - forty1 1 2.0 4125.7 -52044
## - vertical1 1 2.1 4125.9 -52043
## - SD 1 2.7 4126.5 -52039
## - DAL 1 2.9 4126.7 -52037
## - NOR 1 3.0 4126.8 -52037
## - avg_rectd_plyr 1 4.3 4128.0 -52028
## - NE 1 5.0 4128.8 -52023
## - weight 1 5.7 4129.4 -52019
## - avg_rbry_plyr 1 7.0 4130.7 -52010
## - GB 1 7.7 4131.5 -52005
## - height 1 14.3 4138.1 -51961
## - avg_fuml_plyr 1 74.5 4198.2 -51565
## - avg_qbtdp_plyr 1 7702.8 11826.6 -23100
##
## Step: AIC=-52056.23
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + KC + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - JAC 1 0.1 4123.9 -52058
## - DET 1 0.1 4123.9 -52058
## - grass_1 1 0.1 4123.9 -52057
## - hot_weather 1 0.1 4124.0 -52057
## - TEN 1 0.2 4124.0 -52057
## - home_team_1 1 0.2 4124.0 -52057
## - MINN 1 0.2 4124.1 -52057
## - NYJ 1 0.2 4124.1 -52057
## - KC 1 0.3 4124.1 -52056
## <none> 4123.8 -52056
## - OAK 1 0.3 4124.2 -52056
## - DEN 1 0.4 4124.2 -52056
## - CHI 1 0.4 4124.2 -52055
## - ATL 1 0.4 4124.3 -52055
## - TB 1 0.6 4124.5 -52054
## - IND 1 0.8 4124.6 -52053
## - bad_weather_1 1 0.8 4124.6 -52053
## - CLE 1 0.8 4124.6 -52053
## - CIN 1 0.9 4124.7 -52052
## - WAS 1 1.1 4124.9 -52051
## - PHI 1 1.2 4125.1 -52050
## - HOU 1 1.3 4125.1 -52050
## - cold_weather 1 1.3 4125.1 -52049
## - avg_rbry_pos 1 1.5 4125.4 -52048
## - NYG 1 1.8 4125.7 -52046
## - forty1 1 2.0 4125.8 -52045
## - vertical1 1 2.1 4126.0 -52044
## - SD 1 2.6 4126.5 -52041
## - DAL 1 2.8 4126.7 -52039
## - NOR 1 3.0 4126.8 -52038
## - avg_rectd_plyr 1 4.3 4128.1 -52030
## - NE 1 4.9 4128.8 -52025
## - weight 1 5.7 4129.6 -52020
## - avg_rbry_plyr 1 7.0 4130.8 -52012
## - GB 1 7.7 4131.5 -52007
## - height 1 14.4 4138.2 -51963
## - avg_fuml_plyr 1 74.6 4198.5 -51565
## - avg_qbtdp_plyr 1 7704.2 11828.1 -23099
##
## Step: AIC=-52057.74
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DET 1 0.1 4124.0 -52059
## - hot_weather 1 0.1 4124.0 -52059
## - grass_1 1 0.1 4124.0 -52059
## - TEN 1 0.1 4124.0 -52059
## - home_team_1 1 0.2 4124.1 -52059
## - NYJ 1 0.2 4124.1 -52058
## - MINN 1 0.3 4124.2 -52058
## - OAK 1 0.3 4124.2 -52058
## <none> 4123.9 -52058
## - KC 1 0.3 4124.2 -52058
## - DEN 1 0.3 4124.2 -52058
## - CHI 1 0.4 4124.3 -52057
## - ATL 1 0.4 4124.3 -52057
## - TB 1 0.6 4124.5 -52056
## - IND 1 0.7 4124.6 -52055
## - bad_weather_1 1 0.8 4124.7 -52055
## - CIN 1 0.9 4124.8 -52054
## - CLE 1 0.9 4124.8 -52054
## - WAS 1 1.2 4125.1 -52052
## - cold_weather 1 1.3 4125.2 -52051
## - PHI 1 1.3 4125.2 -52051
## - HOU 1 1.3 4125.2 -52051
## - avg_rbry_pos 1 1.5 4125.4 -52050
## - NYG 1 1.8 4125.7 -52048
## - forty1 1 1.9 4125.9 -52047
## - vertical1 1 2.2 4126.1 -52045
## - SD 1 2.6 4126.5 -52043
## - DAL 1 2.8 4126.7 -52041
## - NOR 1 2.9 4126.8 -52040
## - avg_rectd_plyr 1 4.3 4128.2 -52031
## - NE 1 4.9 4128.8 -52027
## - weight 1 5.7 4129.6 -52022
## - avg_rbry_plyr 1 7.0 4130.9 -52013
## - GB 1 7.6 4131.5 -52009
## - height 1 14.4 4138.3 -51964
## - avg_fuml_plyr 1 74.7 4198.6 -51566
## - avg_qbtdp_plyr 1 7704.3 11828.2 -23100
##
## Step: AIC=-52059.21
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN +
## GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + SD + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TEN 1 0.1 4124.1 -52060
## - grass_1 1 0.1 4124.1 -52060
## - hot_weather 1 0.1 4124.1 -52060
## - home_team_1 1 0.2 4124.2 -52060
## - NYJ 1 0.2 4124.2 -52060
## - OAK 1 0.3 4124.3 -52059
## <none> 4124.0 -52059
## - MINN 1 0.3 4124.3 -52059
## - DEN 1 0.3 4124.3 -52059
## - KC 1 0.3 4124.3 -52059
## - CHI 1 0.4 4124.3 -52059
## - ATL 1 0.4 4124.3 -52059
## - TB 1 0.5 4124.5 -52058
## - IND 1 0.7 4124.7 -52057
## - bad_weather_1 1 0.8 4124.8 -52056
## - CIN 1 0.8 4124.8 -52056
## - CLE 1 0.9 4124.9 -52055
## - WAS 1 1.2 4125.2 -52053
## - cold_weather 1 1.2 4125.2 -52053
## - PHI 1 1.4 4125.4 -52052
## - HOU 1 1.4 4125.4 -52052
## - avg_rbry_pos 1 1.5 4125.5 -52051
## - NYG 1 1.7 4125.7 -52050
## - forty1 1 1.9 4125.9 -52048
## - vertical1 1 2.2 4126.2 -52046
## - SD 1 2.5 4126.5 -52044
## - DAL 1 2.7 4126.7 -52043
## - NOR 1 2.8 4126.8 -52042
## - avg_rectd_plyr 1 4.4 4128.3 -52032
## - NE 1 4.8 4128.8 -52029
## - weight 1 5.7 4129.7 -52023
## - avg_rbry_plyr 1 6.9 4130.9 -52015
## - GB 1 7.5 4131.5 -52011
## - height 1 14.4 4138.4 -51965
## - avg_fuml_plyr 1 74.6 4198.6 -51568
## - avg_qbtdp_plyr 1 7704.4 11828.3 -23102
##
## Step: AIC=-52060.44
## py ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN +
## GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.1 4124.2 -52062
## - grass_1 1 0.1 4124.2 -52061
## - home_team_1 1 0.2 4124.3 -52061
## - NYJ 1 0.2 4124.3 -52061
## - OAK 1 0.2 4124.3 -52061
## - DEN 1 0.3 4124.4 -52061
## <none> 4124.1 -52060
## - CHI 1 0.3 4124.4 -52060
## - MINN 1 0.3 4124.4 -52060
## - ATL 1 0.3 4124.4 -52060
## - KC 1 0.4 4124.5 -52060
## - TB 1 0.5 4124.6 -52059
## - IND 1 0.6 4124.7 -52058
## - bad_weather_1 1 0.8 4124.9 -52057
## - CIN 1 0.8 4124.9 -52057
## - CLE 1 1.0 4125.1 -52056
## - cold_weather 1 1.2 4125.3 -52054
## - WAS 1 1.3 4125.4 -52054
## - PHI 1 1.5 4125.6 -52053
## - HOU 1 1.5 4125.6 -52053
## - avg_rbry_pos 1 1.5 4125.6 -52052
## - NYG 1 1.7 4125.8 -52051
## - forty1 1 1.9 4126.0 -52050
## - vertical1 1 2.3 4126.4 -52047
## - SD 1 2.4 4126.5 -52046
## - DAL 1 2.6 4126.7 -52045
## - NOR 1 2.8 4126.9 -52044
## - avg_rectd_plyr 1 4.3 4128.4 -52034
## - NE 1 4.7 4128.8 -52031
## - weight 1 5.7 4129.8 -52025
## - avg_rbry_plyr 1 6.9 4131.0 -52016
## - GB 1 7.4 4131.5 -52013
## - height 1 14.4 4138.5 -51967
## - avg_fuml_plyr 1 74.5 4198.6 -51570
## - avg_qbtdp_plyr 1 7714.1 11838.2 -23081
##
## Step: AIC=-52061.65
## py ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + GB + HOU +
## IND + KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + SD +
## TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 0.2 4124.4 -52063
## - home_team_1 1 0.2 4124.4 -52063
## - NYJ 1 0.2 4124.4 -52062
## - OAK 1 0.2 4124.5 -52062
## - DEN 1 0.3 4124.5 -52062
## <none> 4124.2 -52062
## - CHI 1 0.3 4124.5 -52061
## - ATL 1 0.3 4124.6 -52061
## - MINN 1 0.3 4124.6 -52061
## - KC 1 0.4 4124.6 -52061
## - TB 1 0.5 4124.7 -52060
## - IND 1 0.6 4124.9 -52059
## - bad_weather_1 1 0.7 4125.0 -52059
## - CIN 1 0.8 4125.0 -52058
## - CLE 1 1.0 4125.2 -52057
## - cold_weather 1 1.2 4125.4 -52056
## - WAS 1 1.3 4125.5 -52055
## - PHI 1 1.5 4125.7 -52054
## - HOU 1 1.5 4125.7 -52054
## - avg_rbry_pos 1 1.5 4125.7 -52054
## - NYG 1 1.7 4125.9 -52052
## - forty1 1 1.9 4126.1 -52051
## - vertical1 1 2.3 4126.5 -52049
## - SD 1 2.5 4126.7 -52047
## - DAL 1 2.6 4126.9 -52046
## - NOR 1 2.8 4127.0 -52045
## - avg_rectd_plyr 1 4.3 4128.5 -52035
## - NE 1 4.7 4128.9 -52032
## - weight 1 5.7 4129.9 -52026
## - avg_rbry_plyr 1 6.9 4131.2 -52017
## - GB 1 7.4 4131.6 -52014
## - height 1 14.4 4138.6 -51968
## - avg_fuml_plyr 1 74.5 4198.7 -51571
## - avg_qbtdp_plyr 1 7714.5 11838.8 -23082
##
## Step: AIC=-52062.59
## py ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + GB + HOU +
## IND + KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + SD +
## TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - home_team_1 1 0.1 4124.5 -52064
## - NYJ 1 0.2 4124.5 -52064
## - OAK 1 0.3 4124.7 -52063
## <none> 4124.4 -52063
## - ATL 1 0.3 4124.7 -52063
## - DEN 1 0.3 4124.7 -52062
## - KC 1 0.3 4124.7 -52062
## - CHI 1 0.4 4124.7 -52062
## - MINN 1 0.4 4124.8 -52062
## - TB 1 0.6 4124.9 -52061
## - IND 1 0.6 4125.0 -52061
## - CIN 1 0.7 4125.1 -52060
## - bad_weather_1 1 0.8 4125.1 -52059
## - CLE 1 0.9 4125.3 -52058
## - cold_weather 1 1.2 4125.6 -52056
## - WAS 1 1.3 4125.6 -52056
## - PHI 1 1.4 4125.8 -52055
## - avg_rbry_pos 1 1.5 4125.9 -52054
## - HOU 1 1.5 4125.9 -52054
## - NYG 1 1.6 4126.0 -52054
## - forty1 1 1.9 4126.3 -52052
## - vertical1 1 2.3 4126.6 -52050
## - DAL 1 2.6 4126.9 -52048
## - SD 1 2.7 4127.0 -52047
## - NOR 1 2.7 4127.1 -52047
## - avg_rectd_plyr 1 4.3 4128.7 -52036
## - NE 1 4.6 4129.0 -52034
## - weight 1 5.7 4130.1 -52027
## - avg_rbry_plyr 1 7.0 4131.3 -52018
## - GB 1 7.6 4131.9 -52014
## - height 1 14.4 4138.8 -51969
## - avg_fuml_plyr 1 74.5 4198.9 -51572
## - avg_qbtdp_plyr 1 7714.4 11838.8 -23084
##
## Step: AIC=-52063.82
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + SD + TB + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NYJ 1 0.2 4124.6 -52065
## - OAK 1 0.3 4124.8 -52064
## - DEN 1 0.3 4124.8 -52064
## <none> 4124.5 -52064
## - CHI 1 0.3 4124.8 -52064
## - KC 1 0.4 4124.8 -52063
## - ATL 1 0.4 4124.9 -52063
## - MINN 1 0.4 4124.9 -52063
## - TB 1 0.5 4125.0 -52062
## - IND 1 0.7 4125.1 -52061
## - CIN 1 0.7 4125.2 -52061
## - bad_weather_1 1 0.7 4125.2 -52061
## - CLE 1 1.0 4125.5 -52059
## - cold_weather 1 1.2 4125.7 -52058
## - WAS 1 1.3 4125.8 -52057
## - PHI 1 1.4 4125.9 -52056
## - HOU 1 1.5 4126.0 -52056
## - avg_rbry_pos 1 1.5 4126.0 -52056
## - NYG 1 1.6 4126.1 -52055
## - forty1 1 1.9 4126.4 -52053
## - vertical1 1 2.3 4126.7 -52051
## - SD 1 2.6 4127.1 -52048
## - DAL 1 2.7 4127.2 -52048
## - NOR 1 2.8 4127.3 -52047
## - avg_rectd_plyr 1 4.3 4128.8 -52037
## - NE 1 4.5 4129.0 -52036
## - weight 1 5.7 4130.2 -52028
## - avg_rbry_plyr 1 6.9 4131.4 -52020
## - GB 1 7.5 4132.0 -52016
## - height 1 14.4 4138.9 -51970
## - avg_fuml_plyr 1 74.5 4199.0 -51574
## - avg_qbtdp_plyr 1 7715.0 11839.5 -23084
##
## Step: AIC=-52064.8
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + MINN +
## NE + NOR + NYG + OAK + PHI + SD + TB + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.2 4124.9 -52065
## - DEN 1 0.3 4124.9 -52065
## <none> 4124.6 -52065
## - CHI 1 0.3 4125.0 -52065
## - ATL 1 0.3 4125.0 -52065
## - KC 1 0.4 4125.0 -52064
## - MINN 1 0.4 4125.1 -52064
## - TB 1 0.5 4125.1 -52063
## - IND 1 0.6 4125.3 -52063
## - CIN 1 0.7 4125.3 -52062
## - bad_weather_1 1 0.7 4125.4 -52062
## - CLE 1 1.0 4125.7 -52060
## - cold_weather 1 1.2 4125.9 -52059
## - WAS 1 1.4 4126.0 -52058
## - NYG 1 1.5 4126.2 -52057
## - PHI 1 1.5 4126.2 -52057
## - avg_rbry_pos 1 1.5 4126.2 -52057
## - HOU 1 1.5 4126.2 -52056
## - forty1 1 1.9 4126.5 -52054
## - vertical1 1 2.3 4127.0 -52051
## - SD 1 2.5 4127.2 -52050
## - DAL 1 2.7 4127.3 -52049
## - NOR 1 2.7 4127.3 -52049
## - avg_rectd_plyr 1 4.3 4128.9 -52038
## - NE 1 4.4 4129.1 -52037
## - weight 1 5.7 4130.3 -52029
## - avg_rbry_plyr 1 7.0 4131.6 -52020
## - GB 1 7.4 4132.0 -52018
## - height 1 14.4 4139.0 -51971
## - avg_fuml_plyr 1 74.4 4199.0 -51576
## - avg_qbtdp_plyr 1 7722.0 11846.6 -23070
##
## Step: AIC=-52065.2
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + MINN +
## NE + NOR + NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DEN 1 0.2 4125.1 -52066
## - CHI 1 0.3 4125.2 -52065
## - ATL 1 0.3 4125.2 -52065
## <none> 4124.9 -52065
## - KC 1 0.4 4125.3 -52064
## - TB 1 0.5 4125.3 -52064
## - MINN 1 0.5 4125.4 -52064
## - IND 1 0.6 4125.4 -52063
## - CIN 1 0.6 4125.5 -52063
## - bad_weather_1 1 0.8 4125.6 -52062
## - CLE 1 1.1 4126.0 -52060
## - cold_weather 1 1.2 4126.1 -52059
## - NYG 1 1.4 4126.3 -52058
## - WAS 1 1.5 4126.3 -52058
## - avg_rbry_pos 1 1.5 4126.4 -52057
## - PHI 1 1.6 4126.5 -52057
## - HOU 1 1.7 4126.5 -52056
## - forty1 1 2.0 4126.8 -52054
## - vertical1 1 2.3 4127.2 -52052
## - SD 1 2.4 4127.3 -52051
## - DAL 1 2.6 4127.4 -52050
## - NOR 1 2.6 4127.5 -52050
## - avg_rectd_plyr 1 4.2 4129.1 -52039
## - NE 1 4.3 4129.2 -52038
## - weight 1 5.6 4130.5 -52030
## - avg_rbry_plyr 1 6.9 4131.8 -52021
## - GB 1 7.2 4132.1 -52019
## - height 1 14.2 4139.1 -51973
## - avg_fuml_plyr 1 74.6 4199.5 -51574
## - avg_qbtdp_plyr 1 7721.7 11846.6 -23072
##
## Step: AIC=-52065.64
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + GB + HOU + IND + KC + MINN + NE +
## NOR + NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CHI 1 0.2 4125.4 -52066
## - ATL 1 0.3 4125.4 -52066
## <none> 4125.1 -52066
## - TB 1 0.4 4125.5 -52065
## - KC 1 0.5 4125.6 -52064
## - IND 1 0.5 4125.6 -52064
## - MINN 1 0.5 4125.6 -52064
## - CIN 1 0.6 4125.7 -52064
## - bad_weather_1 1 0.7 4125.9 -52063
## - CLE 1 1.2 4126.3 -52060
## - cold_weather 1 1.2 4126.3 -52060
## - NYG 1 1.4 4126.5 -52059
## - avg_rbry_pos 1 1.5 4126.6 -52058
## - WAS 1 1.5 4126.7 -52057
## - PHI 1 1.7 4126.8 -52056
## - HOU 1 1.7 4126.9 -52056
## - forty1 1 1.9 4127.0 -52055
## - vertical1 1 2.3 4127.5 -52052
## - SD 1 2.4 4127.5 -52052
## - DAL 1 2.5 4127.6 -52051
## - NOR 1 2.5 4127.6 -52051
## - NE 1 4.2 4129.3 -52040
## - avg_rectd_plyr 1 4.3 4129.5 -52039
## - weight 1 5.6 4130.7 -52031
## - avg_rbry_plyr 1 6.9 4132.0 -52022
## - GB 1 7.1 4132.2 -52020
## - height 1 14.3 4139.4 -51973
## - avg_fuml_plyr 1 74.6 4199.7 -51575
## - avg_qbtdp_plyr 1 7722.8 11847.9 -23070
##
## Step: AIC=-52066
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CIN + CLE + DAL + GB + HOU + IND + KC + MINN + NE + NOR +
## NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ATL 1 0.2 4125.6 -52066
## <none> 4125.4 -52066
## - TB 1 0.4 4125.7 -52065
## - IND 1 0.5 4125.8 -52065
## - CIN 1 0.5 4125.9 -52065
## - KC 1 0.5 4125.9 -52064
## - MINN 1 0.6 4125.9 -52064
## - bad_weather_1 1 0.8 4126.1 -52063
## - cold_weather 1 1.3 4126.6 -52060
## - CLE 1 1.3 4126.6 -52060
## - NYG 1 1.3 4126.7 -52059
## - avg_rbry_pos 1 1.5 4126.8 -52058
## - WAS 1 1.6 4127.0 -52057
## - PHI 1 1.8 4127.2 -52056
## - HOU 1 1.8 4127.2 -52056
## - forty1 1 1.9 4127.3 -52055
## - SD 1 2.3 4127.6 -52053
## - vertical1 1 2.3 4127.6 -52053
## - DAL 1 2.4 4127.8 -52052
## - NOR 1 2.4 4127.8 -52052
## - NE 1 4.1 4129.5 -52041
## - avg_rectd_plyr 1 4.3 4129.7 -52039
## - weight 1 5.5 4130.9 -52031
## - GB 1 6.9 4132.3 -52022
## - avg_rbry_plyr 1 6.9 4132.3 -52022
## - height 1 14.1 4139.5 -51974
## - avg_fuml_plyr 1 74.4 4199.8 -51577
## - avg_qbtdp_plyr 1 7733.1 11858.5 -23048
##
## Step: AIC=-52066.44
## py ~ height + weight + cold_weather + forty1 + vertical1 + CIN +
## CLE + DAL + GB + HOU + IND + KC + MINN + NE + NOR + NYG +
## PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## <none> 4125.6 -52066
## - TB 1 0.3 4125.9 -52066
## - IND 1 0.4 4126.0 -52066
## - CIN 1 0.5 4126.1 -52065
## - KC 1 0.6 4126.2 -52065
## - MINN 1 0.6 4126.2 -52064
## - bad_weather_1 1 0.8 4126.4 -52063
## - cold_weather 1 1.2 4126.8 -52061
## - NYG 1 1.2 4126.8 -52060
## - CLE 1 1.3 4126.9 -52060
## - avg_rbry_pos 1 1.5 4127.1 -52059
## - WAS 1 1.7 4127.3 -52057
## - PHI 1 1.9 4127.5 -52056
## - forty1 1 1.9 4127.5 -52056
## - HOU 1 1.9 4127.5 -52056
## - SD 1 2.2 4127.8 -52054
## - vertical1 1 2.2 4127.8 -52054
## - DAL 1 2.3 4127.9 -52053
## - NOR 1 2.3 4127.9 -52053
## - NE 1 4.0 4129.6 -52042
## - avg_rectd_plyr 1 4.5 4130.1 -52039
## - weight 1 5.5 4131.1 -52032
## - GB 1 6.8 4132.4 -52023
## - avg_rbry_plyr 1 7.0 4132.6 -52022
## - height 1 14.3 4139.9 -51973
## - avg_fuml_plyr 1 75.1 4200.7 -51573
## - avg_qbtdp_plyr 1 7746.2 11871.8 -23019Conclusion, this predicts well, but it seems like this could be driven by some chance. QB statistics remind me of baseball statistics. One batter vs One pitcher. A QB is really like a pitcher or a batter. The opponent is more complex, however one side of the equation is “controlled”.
Pass completions
PreProcess:
set.seed(123)
splitpc <- sample.split(nfl_data$pc, SplitRatio = 0.7)
Trainpc <- subset(nfl_data, split == TRUE)
Testpc <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainpc, method = c("center", "scale"))
trainTransformedpc <- predict(preProcValues, Trainpc)
testTransformedpc <- predict(preProcValues, Testpc)ggpairs:
ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[46:51]))])
pcregform <- formula(paste("pc ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegQBpc <- lm(pcregform, data = trainTransformedpc)
summary(linRegQBpc)##
## Call:
## lm(formula = pcregform, data = trainTransformedpc)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2064 -0.0581 -0.0134 0.0334 4.6794
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.619e-16 2.292e-03 0.000 1.00000
## height 4.875e-02 4.447e-03 10.962 < 2e-16 ***
## weight -3.307e-02 4.168e-03 -7.934 2.20e-15 ***
## cold_weather -6.023e-03 2.413e-03 -2.497 0.01255 *
## hot_weather -1.998e-03 2.313e-03 -0.864 0.38767
## home_team_1 -4.305e-04 2.494e-03 -0.173 0.86295
## forty1 1.912e-02 3.956e-03 4.834 1.34e-06 ***
## vertical1 -1.573e-02 3.041e-03 -5.171 2.35e-07 ***
## ARI -5.917e-04 3.206e-03 -0.185 0.85358
## ATL -4.000e-03 3.222e-03 -1.242 0.21435
## BAL 7.475e-05 3.224e-03 0.023 0.98150
## BUF 1.988e-03 3.183e-03 0.624 0.53234
## CAR -3.205e-03 3.162e-03 -1.013 0.31086
## CHI -4.804e-03 3.127e-03 -1.536 0.12448
## CIN -3.230e-03 3.184e-03 -1.014 0.31044
## CLE 7.483e-03 3.170e-03 2.361 0.01824 *
## DAL -1.007e-02 3.202e-03 -3.144 0.00167 **
## DEN -5.680e-03 3.214e-03 -1.767 0.07723 .
## DET -2.677e-03 3.170e-03 -0.844 0.39848
## GB -1.886e-02 3.263e-03 -5.779 7.61e-09 ***
## HOU 7.485e-03 3.224e-03 2.321 0.02028 *
## IND -5.768e-03 3.201e-03 -1.802 0.07155 .
## JAC 1.020e-03 3.122e-03 0.327 0.74386
## KC 6.030e-03 3.191e-03 1.890 0.05880 .
## MIA 5.780e-04 3.139e-03 0.184 0.85392
## MINN 6.798e-03 3.159e-03 2.152 0.03140 *
## NE -1.660e-02 3.299e-03 -5.031 4.91e-07 ***
## NOR -8.839e-03 3.289e-03 -2.688 0.00720 **
## NYG -9.940e-03 3.214e-03 -3.092 0.00199 **
## NYJ -3.931e-03 3.203e-03 -1.227 0.21971
## OAK -3.317e-03 3.223e-03 -1.029 0.30332
## PHI 5.894e-03 3.123e-03 1.887 0.05911 .
## PIT -2.766e-03 3.205e-03 -0.863 0.38812
## SD -1.241e-02 3.145e-03 -3.945 7.98e-05 ***
## SEA -6.289e-05 3.264e-03 -0.019 0.98463
## STL 2.845e-03 3.177e-03 0.896 0.37046
## TB -6.705e-03 3.147e-03 -2.130 0.03314 *
## TEN -4.097e-03 3.166e-03 -1.294 0.19569
## WAS 5.572e-03 3.183e-03 1.751 0.08002 .
## avg_trg_team NA NA NA NA
## avg_rectd_plyr -1.563e-02 2.927e-03 -5.340 9.35e-08 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr -3.018e-02 3.503e-03 -8.616 < 2e-16 ***
## avg_rbry_pos 1.899e-02 4.081e-03 4.654 3.27e-06 ***
## avg_fuml_plyr 7.949e-02 3.386e-03 23.477 < 2e-16 ***
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr 8.437e-01 3.678e-03 229.388 < 2e-16 ***
## avg_qbtdp_team NA NA NA NA
## grass_1 -1.757e-03 2.637e-03 -0.666 0.50524
## bad_weather_1 -5.132e-03 2.332e-03 -2.201 0.02775 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.38 on 27438 degrees of freedom
## Multiple R-squared: 0.8558, Adjusted R-squared: 0.8556
## F-statistic: 3620 on 45 and 27438 DF, p-value: < 2.2e-16linRegQBpc2 <- update(linRegQBpc, ~.-hot_weather-home_team_1-vertical1-ATL-BAL-CIN-DAL-DEN-DET-KC
-MIA-PHI-PIT-SEA-STL-WAS-avg_trg_team-avg_tdr_team-avg_rbra_team
-avg_rbry_plyr-avg_fuml_team-avg_qbints_team-avg_qbtdp_team-grass_1 )
summary(linRegQBpc2)##
## Call:
## lm(formula = pc ~ height + weight + cold_weather + forty1 + ARI +
## BUF + CAR + CHI + CLE + GB + HOU + IND + JAC + MINN + NE +
## NOR + NYG + NYJ + OAK + SD + TB + TEN + avg_rectd_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1,
## data = trainTransformedpc)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2398 -0.0575 -0.0124 0.0294 4.6660
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.666e-16 2.298e-03 0.000 1.000000
## height 4.709e-02 4.435e-03 10.619 < 2e-16 ***
## weight -3.546e-02 4.143e-03 -8.558 < 2e-16 ***
## cold_weather -5.546e-03 2.366e-03 -2.344 0.019063 *
## forty1 3.370e-02 3.324e-03 10.139 < 2e-16 ***
## ARI 1.021e-03 2.347e-03 0.435 0.663685
## BUF 3.111e-03 2.346e-03 1.326 0.184868
## CAR -3.434e-03 2.345e-03 -1.464 0.143092
## CHI -4.221e-03 2.347e-03 -1.798 0.072184 .
## CLE 7.582e-03 2.354e-03 3.221 0.001279 **
## GB -1.833e-02 2.367e-03 -7.744 9.98e-15 ***
## HOU 7.470e-03 2.354e-03 3.173 0.001512 **
## IND -5.380e-03 2.344e-03 -2.295 0.021764 *
## JAC 6.082e-04 2.343e-03 0.260 0.795205
## MINN 6.319e-03 2.350e-03 2.689 0.007163 **
## NE -1.631e-02 2.395e-03 -6.809 1.00e-11 ***
## NOR -7.575e-03 2.363e-03 -3.205 0.001350 **
## NYG -8.832e-03 2.348e-03 -3.761 0.000169 ***
## NYJ -4.421e-03 2.345e-03 -1.885 0.059386 .
## OAK -1.986e-03 2.360e-03 -0.841 0.400133
## SD -1.167e-02 2.347e-03 -4.973 6.63e-07 ***
## TB -6.022e-03 2.346e-03 -2.568 0.010247 *
## TEN -3.866e-03 2.346e-03 -1.648 0.099462 .
## avg_rectd_plyr -1.860e-02 2.908e-03 -6.396 1.62e-10 ***
## avg_rbry_pos -5.369e-04 3.417e-03 -0.157 0.875164
## avg_fuml_plyr 7.127e-02 3.185e-03 22.374 < 2e-16 ***
## avg_qbtdp_plyr 8.468e-01 3.635e-03 232.924 < 2e-16 ***
## bad_weather_1 -5.320e-03 2.332e-03 -2.281 0.022535 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3809 on 27456 degrees of freedom
## Multiple R-squared: 0.855, Adjusted R-squared: 0.8549
## F-statistic: 5998 on 27 and 27456 DF, p-value: < 2.2e-16Again, R2 is very strong, model stays strong when model is shrunk to 8 variables. Not surprising (to me) bad weather and cold weather hurt completions. It is harder to throw a ball in bad weather and catch a ball in bad weather.
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
PcPredicted <- predict(linRegQBpc2, newdata = testTransformedpc)
SSEpc <- sum((PcPredicted - testTransformedpc$pc)^2)
SSTpc <- sum((mean(nfl_data$pc)-testTransformedpc$pc)^2)
r2_pc <- 1 - SSEpc/SSTpc
r2_pc## [1] 0.9703489rmse_pc <- sqrt(SSEpc/nrow(testTransformedpc))
rmse_pc## [1] 0.3924396Regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBpc2, which = c(1:3,5))
Very similar problems/characteristics as we saw in yards
Summary statistics:
confint(linRegQBpc2)## 2.5 % 97.5 %
## (Intercept) -0.004503758 0.0045037581
## height 0.038398997 0.0557838535
## weight -0.043577952 -0.0273367386
## cold_weather -0.010182362 -0.0009092848
## forty1 0.027185053 0.0402147931
## ARI -0.003579930 0.0056211955
## BUF -0.001487868 0.0077103207
## CAR -0.008031261 0.0011623957
## CHI -0.008821661 0.0003803371
## CLE 0.002968402 0.0121965425
## GB -0.022967535 -0.0136892607
## HOU 0.002855127 0.0120843132
## IND -0.009974835 -0.0007843123
## JAC -0.003984834 0.0052013096
## MINN 0.001713726 0.0109249709
## NE -0.020998638 -0.0116116817
## NOR -0.012207381 -0.0029431848
## NYG -0.013434167 -0.0042295072
## NYJ -0.009016369 0.0001750304
## OAK -0.006612556 0.0026404775
## SD -0.016274935 -0.0070726373
## TB -0.010619902 -0.0014249439
## TEN -0.008464463 0.0007332893
## avg_rectd_plyr -0.024300118 -0.0129002712
## avg_rbry_pos -0.007235219 0.0061614368
## avg_fuml_plyr 0.065021908 0.0775083344
## avg_qbtdp_plyr 0.839643262 0.8538943403
## bad_weather_1 -0.009890038 -0.0007491984coef(summary(linRegQBpc2))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.666331e-16 0.002297777 3.336412e-13 1.000000e+00
## height 4.709143e-02 0.004434798 1.061862e+01 2.745893e-26
## weight -3.545735e-02 0.004143060 -8.558250e+00 1.204789e-17
## cold_weather -5.545823e-03 0.002365520 -2.344441e+00 1.906269e-02
## forty1 3.369992e-02 0.003323828 1.013889e+01 4.094619e-24
## ARI 1.020633e-03 0.002347165 4.348364e-01 6.636846e-01
## BUF 3.111226e-03 0.002346417 1.325948e+00 1.848680e-01
## CAR -3.434433e-03 0.002345260 -1.464414e+00 1.430922e-01
## CHI -4.220662e-03 0.002347388 -1.798025e+00 7.218407e-02
## CLE 7.582472e-03 0.002354057 3.221023e+00 1.278825e-03
## GB -1.832840e-02 0.002366846 -7.743807e+00 9.979816e-15
## HOU 7.469720e-03 0.002354324 3.172767e+00 1.511602e-03
## IND -5.379574e-03 0.002344461 -2.294589e+00 2.176421e-02
## JAC 6.082379e-04 0.002343344 2.595598e-01 7.952053e-01
## MINN 6.319349e-03 0.002349747 2.689374e+00 7.162938e-03
## NE -1.630516e-02 0.002394570 -6.809222e+00 1.001490e-11
## NOR -7.575283e-03 0.002363254 -3.205445e+00 1.350080e-03
## NYG -8.831837e-03 0.002348067 -3.761322e+00 1.693684e-04
## NYJ -4.420669e-03 0.002344684 -1.885400e+00 5.938634e-02
## OAK -1.986039e-03 0.002360407 -8.413970e-01 4.001329e-01
## SD -1.167379e-02 0.002347465 -4.972934e+00 6.634458e-07
## TB -6.022423e-03 0.002345592 -2.567549e+00 1.024728e-02
## TEN -3.865587e-03 0.002346305 -1.647521e+00 9.946244e-02
## avg_rectd_plyr -1.860019e-02 0.002908049 -6.396107e+00 1.619528e-10
## avg_rbry_pos -5.368910e-04 0.003417426 -1.571039e-01 8.751641e-01
## avg_fuml_plyr 7.126512e-02 0.003185231 2.237361e+01 6.839892e-110
## avg_qbtdp_plyr 8.467688e-01 0.003635386 2.329241e+02 0.000000e+00
## bad_weather_1 -5.319618e-03 0.002331787 -2.281348e+00 2.253546e-02anova(linRegQBpc2)## Analysis of Variance Table
##
## Response: pc
## Df Sum Sq Mean Sq F value Pr(>F)
## height 1 1882.8 1882.8 12974.7620 < 2.2e-16 ***
## weight 1 461.2 461.2 3178.5347 < 2.2e-16 ***
## cold_weather 1 0.5 0.5 3.7567 0.052607 .
## forty1 1 5589.0 5589.0 38515.7304 < 2.2e-16 ***
## ARI 1 0.3 0.3 2.1068 0.146660
## BUF 1 0.9 0.9 6.3007 0.012075 *
## CAR 1 6.9 6.9 47.7623 4.917e-12 ***
## CHI 1 0.2 0.2 1.2414 0.265216
## CLE 1 1.1 1.1 7.2861 0.006953 **
## GB 1 0.0 0.0 0.0309 0.860535
## HOU 1 13.9 13.9 95.9656 < 2.2e-16 ***
## IND 1 11.5 11.5 79.0848 < 2.2e-16 ***
## JAC 1 0.1 0.1 0.9519 0.329253
## MINN 1 0.4 0.4 2.9212 0.087437 .
## NE 1 36.9 36.9 254.3033 < 2.2e-16 ***
## NOR 1 16.0 16.0 110.5203 < 2.2e-16 ***
## NYG 1 6.4 6.4 43.9986 3.347e-11 ***
## NYJ 1 0.4 0.4 3.0309 0.081702 .
## OAK 1 0.8 0.8 5.7241 0.016740 *
## SD 1 12.4 12.4 85.4687 < 2.2e-16 ***
## TB 1 2.3 2.3 15.6288 7.727e-05 ***
## TEN 1 4.4 4.4 30.1061 4.127e-08 ***
## avg_rectd_plyr 1 1862.7 1862.7 12836.4447 < 2.2e-16 ***
## avg_rbry_pos 1 322.4 322.4 2221.7472 < 2.2e-16 ***
## avg_fuml_plyr 1 5391.9 5391.9 37157.5723 < 2.2e-16 ***
## avg_qbtdp_plyr 1 7872.6 7872.6 54252.8371 < 2.2e-16 ***
## bad_weather_1 1 0.8 0.8 5.2046 0.022535 *
## Residuals 27456 3984.1 0.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_pc <- step(lm(pcregform, data = trainTransformedpc), direction = "backward")## Start: AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.0 3961.8 -53144
## - BAL 1 0.0 3961.8 -53144
## - home_team_1 1 0.0 3961.8 -53144
## - MIA 1 0.0 3961.8 -53144
## - ARI 1 0.0 3961.8 -53144
## - JAC 1 0.0 3961.9 -53144
## - BUF 1 0.1 3961.9 -53143
## - grass_1 1 0.1 3961.9 -53143
## - DET 1 0.1 3961.9 -53143
## - PIT 1 0.1 3961.9 -53143
## - hot_weather 1 0.1 3961.9 -53143
## - STL 1 0.1 3962.0 -53143
## - CAR 1 0.1 3962.0 -53143
## - CIN 1 0.1 3962.0 -53143
## - OAK 1 0.2 3962.0 -53143
## - NYJ 1 0.2 3962.1 -53142
## - ATL 1 0.2 3962.1 -53142
## - TEN 1 0.2 3962.1 -53142
## <none> 3961.8 -53142
## - CHI 1 0.3 3962.2 -53141
## - WAS 1 0.4 3962.3 -53141
## - DEN 1 0.5 3962.3 -53141
## - IND 1 0.5 3962.3 -53140
## - PHI 1 0.5 3962.4 -53140
## - KC 1 0.5 3962.4 -53140
## - TB 1 0.7 3962.5 -53139
## - MINN 1 0.7 3962.5 -53139
## - bad_weather_1 1 0.7 3962.5 -53139
## - HOU 1 0.8 3962.6 -53138
## - CLE 1 0.8 3962.6 -53138
## - cold_weather 1 0.9 3962.7 -53137
## - NOR 1 1.0 3962.9 -53136
## - NYG 1 1.4 3963.2 -53134
## - DAL 1 1.4 3963.3 -53134
## - SD 1 2.2 3964.1 -53128
## - avg_rbry_pos 1 3.1 3965.0 -53122
## - forty1 1 3.4 3965.2 -53120
## - NE 1 3.7 3965.5 -53118
## - vertical1 1 3.9 3965.7 -53117
## - avg_rectd_plyr 1 4.1 3966.0 -53115
## - GB 1 4.8 3966.7 -53110
## - weight 1 9.1 3970.9 -53081
## - avg_rbry_plyr 1 10.7 3972.6 -53069
## - height 1 17.4 3979.2 -53024
## - avg_fuml_plyr 1 79.6 4041.4 -52597
## - avg_qbtdp_plyr 1 7597.8 11559.6 -23714
##
## Step: AIC=-53143.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BAL 1 0.0 3961.8 -53146
## - home_team_1 1 0.0 3961.8 -53146
## - ARI 1 0.0 3961.8 -53146
## - MIA 1 0.0 3961.8 -53146
## - JAC 1 0.0 3961.9 -53145
## - grass_1 1 0.1 3961.9 -53145
## - BUF 1 0.1 3961.9 -53145
## - hot_weather 1 0.1 3961.9 -53145
## - DET 1 0.1 3962.0 -53145
## - PIT 1 0.1 3962.0 -53145
## - STL 1 0.2 3962.0 -53145
## - CAR 1 0.2 3962.0 -53144
## - CIN 1 0.2 3962.0 -53144
## - OAK 1 0.2 3962.0 -53144
## <none> 3961.8 -53144
## - NYJ 1 0.3 3962.1 -53144
## - ATL 1 0.3 3962.1 -53144
## - TEN 1 0.3 3962.2 -53143
## - CHI 1 0.4 3962.3 -53143
## - WAS 1 0.6 3962.4 -53142
## - DEN 1 0.6 3962.4 -53142
## - IND 1 0.6 3962.5 -53141
## - PHI 1 0.7 3962.5 -53141
## - KC 1 0.7 3962.5 -53141
## - bad_weather_1 1 0.7 3962.5 -53141
## - TB 1 0.9 3962.7 -53140
## - MINN 1 0.9 3962.7 -53139
## - cold_weather 1 0.9 3962.7 -53139
## - HOU 1 1.0 3962.9 -53138
## - CLE 1 1.1 3962.9 -53138
## - NOR 1 1.4 3963.3 -53136
## - NYG 1 1.9 3963.7 -53133
## - DAL 1 1.9 3963.7 -53133
## - SD 1 2.9 3964.8 -53125
## - avg_rbry_pos 1 3.1 3965.0 -53124
## - forty1 1 3.4 3965.2 -53122
## - vertical1 1 3.9 3965.7 -53119
## - avg_rectd_plyr 1 4.1 3966.0 -53117
## - NE 1 5.0 3966.8 -53111
## - GB 1 6.5 3968.3 -53101
## - weight 1 9.1 3970.9 -53083
## - avg_rbry_plyr 1 10.7 3972.6 -53071
## - height 1 17.4 3979.2 -53026
## - avg_fuml_plyr 1 79.6 4041.5 -52599
## - avg_qbtdp_plyr 1 7604.3 11566.1 -23700
##
## Step: AIC=-53145.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - home_team_1 1 0.0 3961.8 -53148
## - MIA 1 0.0 3961.8 -53148
## - ARI 1 0.0 3961.8 -53148
## - JAC 1 0.0 3961.9 -53147
## - grass_1 1 0.1 3961.9 -53147
## - BUF 1 0.1 3961.9 -53147
## - hot_weather 1 0.1 3961.9 -53147
## - DET 1 0.2 3962.0 -53147
## - PIT 1 0.2 3962.0 -53147
## - STL 1 0.2 3962.0 -53146
## - CAR 1 0.2 3962.1 -53146
## - CIN 1 0.2 3962.1 -53146
## - OAK 1 0.2 3962.1 -53146
## <none> 3961.8 -53146
## - NYJ 1 0.3 3962.2 -53145
## - ATL 1 0.3 3962.2 -53145
## - TEN 1 0.4 3962.2 -53145
## - CHI 1 0.5 3962.3 -53144
## - WAS 1 0.7 3962.5 -53143
## - DEN 1 0.7 3962.5 -53143
## - bad_weather_1 1 0.7 3962.5 -53143
## - IND 1 0.7 3962.5 -53143
## - PHI 1 0.7 3962.6 -53142
## - KC 1 0.8 3962.6 -53142
## - cold_weather 1 0.9 3962.7 -53141
## - TB 1 1.0 3962.8 -53141
## - MINN 1 1.0 3962.8 -53141
## - HOU 1 1.2 3963.0 -53140
## - CLE 1 1.2 3963.0 -53139
## - NOR 1 1.6 3963.4 -53136
## - NYG 1 2.1 3963.9 -53133
## - DAL 1 2.1 3964.0 -53133
## - avg_rbry_pos 1 3.1 3965.0 -53126
## - SD 1 3.3 3965.1 -53125
## - forty1 1 3.4 3965.2 -53124
## - vertical1 1 3.9 3965.7 -53121
## - avg_rectd_plyr 1 4.1 3966.0 -53119
## - NE 1 5.6 3967.4 -53109
## - GB 1 7.3 3969.2 -53097
## - weight 1 9.1 3970.9 -53085
## - avg_rbry_plyr 1 10.7 3972.6 -53073
## - height 1 17.4 3979.2 -53027
## - avg_fuml_plyr 1 79.6 4041.5 -52601
## - avg_qbtdp_plyr 1 7605.8 11567.7 -23698
##
## Step: AIC=-53147.6
## pc ~ height + weight + cold_weather + hot_weather + forty1 +
## vertical1 + ARI + ATL + BUF + CAR + CHI + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ARI 1 0.0 3961.9 -53150
## - MIA 1 0.0 3961.9 -53150
## - JAC 1 0.0 3961.9 -53149
## - grass_1 1 0.1 3961.9 -53149
## - BUF 1 0.1 3961.9 -53149
## - hot_weather 1 0.1 3962.0 -53149
## - DET 1 0.1 3962.0 -53149
## - PIT 1 0.2 3962.0 -53148
## - STL 1 0.2 3962.0 -53148
## - CAR 1 0.2 3962.1 -53148
## - CIN 1 0.2 3962.1 -53148
## - OAK 1 0.2 3962.1 -53148
## <none> 3961.8 -53148
## - ATL 1 0.3 3962.2 -53147
## - NYJ 1 0.3 3962.2 -53147
## - TEN 1 0.4 3962.2 -53147
## - CHI 1 0.5 3962.3 -53146
## - WAS 1 0.7 3962.5 -53145
## - DEN 1 0.7 3962.5 -53145
## - IND 1 0.7 3962.5 -53145
## - bad_weather_1 1 0.7 3962.5 -53145
## - PHI 1 0.7 3962.6 -53144
## - KC 1 0.8 3962.6 -53144
## - cold_weather 1 0.9 3962.8 -53143
## - TB 1 1.0 3962.8 -53143
## - MINN 1 1.0 3962.8 -53143
## - CLE 1 1.2 3963.0 -53141
## - HOU 1 1.2 3963.0 -53141
## - NOR 1 1.6 3963.4 -53138
## - NYG 1 2.1 3963.9 -53135
## - DAL 1 2.1 3964.0 -53135
## - avg_rbry_pos 1 3.1 3965.0 -53128
## - SD 1 3.3 3965.1 -53127
## - forty1 1 3.4 3965.2 -53126
## - vertical1 1 3.9 3965.7 -53123
## - avg_rectd_plyr 1 4.1 3966.0 -53121
## - NE 1 5.6 3967.5 -53111
## - GB 1 7.3 3969.2 -53099
## - weight 1 9.1 3970.9 -53087
## - avg_rbry_plyr 1 10.7 3972.6 -53075
## - height 1 17.4 3979.2 -53029
## - avg_fuml_plyr 1 79.6 4041.5 -52603
## - avg_qbtdp_plyr 1 7606.0 11567.8 -23700
##
## Step: AIC=-53149.56
## pc ~ height + weight + cold_weather + hot_weather + forty1 +
## vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR +
## NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.0 3961.9 -53151
## - JAC 1 0.0 3961.9 -53151
## - grass_1 1 0.1 3961.9 -53151
## - BUF 1 0.1 3962.0 -53151
## - hot_weather 1 0.1 3962.0 -53151
## - DET 1 0.1 3962.0 -53151
## - PIT 1 0.2 3962.0 -53150
## - STL 1 0.2 3962.1 -53150
## - CAR 1 0.2 3962.1 -53150
## - CIN 1 0.2 3962.1 -53150
## - OAK 1 0.2 3962.1 -53150
## <none> 3961.9 -53150
## - ATL 1 0.3 3962.2 -53149
## - NYJ 1 0.3 3962.2 -53149
## - TEN 1 0.4 3962.2 -53149
## - CHI 1 0.5 3962.3 -53148
## - DEN 1 0.7 3962.5 -53147
## - bad_weather_1 1 0.7 3962.6 -53147
## - IND 1 0.7 3962.6 -53147
## - WAS 1 0.7 3962.6 -53147
## - PHI 1 0.8 3962.7 -53146
## - KC 1 0.8 3962.7 -53146
## - cold_weather 1 0.9 3962.8 -53145
## - TB 1 1.0 3962.8 -53145
## - MINN 1 1.1 3962.9 -53144
## - CLE 1 1.3 3963.1 -53143
## - HOU 1 1.3 3963.2 -53142
## - NOR 1 1.7 3963.5 -53140
## - NYG 1 2.2 3964.0 -53136
## - DAL 1 2.2 3964.1 -53136
## - avg_rbry_pos 1 3.1 3965.0 -53130
## - SD 1 3.4 3965.2 -53128
## - forty1 1 3.4 3965.2 -53128
## - vertical1 1 3.9 3965.7 -53125
## - avg_rectd_plyr 1 4.1 3966.0 -53123
## - NE 1 5.8 3967.7 -53111
## - GB 1 7.7 3969.5 -53098
## - weight 1 9.1 3970.9 -53089
## - avg_rbry_plyr 1 10.7 3972.6 -53077
## - height 1 17.4 3979.2 -53031
## - avg_fuml_plyr 1 79.7 4041.5 -52604
## - avg_qbtdp_plyr 1 7617.6 11579.4 -23674
##
## Step: AIC=-53151.48
## pc ~ height + weight + cold_weather + hot_weather + forty1 +
## vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + KC + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - JAC 1 0.0 3961.9 -53153
## - grass_1 1 0.1 3961.9 -53153
## - BUF 1 0.1 3962.0 -53153
## - hot_weather 1 0.1 3962.0 -53153
## - DET 1 0.2 3962.0 -53152
## - PIT 1 0.2 3962.0 -53152
## - STL 1 0.2 3962.1 -53152
## - CAR 1 0.2 3962.1 -53152
## - CIN 1 0.2 3962.1 -53152
## - OAK 1 0.3 3962.1 -53152
## <none> 3961.9 -53151
## - ATL 1 0.4 3962.2 -53151
## - NYJ 1 0.4 3962.2 -53151
## - TEN 1 0.4 3962.3 -53151
## - CHI 1 0.5 3962.4 -53150
## - bad_weather_1 1 0.7 3962.6 -53149
## - WAS 1 0.7 3962.6 -53149
## - DEN 1 0.8 3962.6 -53148
## - IND 1 0.8 3962.6 -53148
## - PHI 1 0.8 3962.7 -53148
## - KC 1 0.8 3962.7 -53148
## - cold_weather 1 0.9 3962.8 -53147
## - TB 1 1.1 3962.9 -53146
## - MINN 1 1.1 3963.0 -53146
## - CLE 1 1.3 3963.2 -53145
## - HOU 1 1.3 3963.2 -53144
## - NOR 1 1.8 3963.6 -53141
## - NYG 1 2.3 3964.2 -53137
## - DAL 1 2.4 3964.2 -53137
## - avg_rbry_pos 1 3.1 3965.0 -53132
## - forty1 1 3.4 3965.3 -53130
## - SD 1 3.6 3965.5 -53129
## - vertical1 1 3.9 3965.7 -53127
## - avg_rectd_plyr 1 4.1 3966.0 -53125
## - NE 1 6.2 3968.0 -53111
## - GB 1 8.1 3970.0 -53097
## - weight 1 9.1 3971.0 -53090
## - avg_rbry_plyr 1 10.8 3972.6 -53079
## - height 1 17.4 3979.3 -53033
## - avg_fuml_plyr 1 79.8 4041.7 -52605
## - avg_qbtdp_plyr 1 7623.0 11584.9 -23663
##
## Step: AIC=-53153.32
## pc ~ height + weight + cold_weather + hot_weather + forty1 +
## vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 0.1 3961.9 -53155
## - BUF 1 0.1 3962.0 -53155
## - hot_weather 1 0.1 3962.0 -53155
## - STL 1 0.2 3962.1 -53154
## - DET 1 0.2 3962.1 -53154
## - PIT 1 0.2 3962.1 -53154
## - CIN 1 0.3 3962.2 -53153
## - CAR 1 0.3 3962.2 -53153
## <none> 3961.9 -53153
## - OAK 1 0.3 3962.2 -53153
## - ATL 1 0.4 3962.3 -53153
## - NYJ 1 0.4 3962.3 -53153
## - TEN 1 0.4 3962.3 -53152
## - CHI 1 0.6 3962.5 -53151
## - WAS 1 0.7 3962.6 -53150
## - bad_weather_1 1 0.7 3962.6 -53150
## - PHI 1 0.8 3962.7 -53150
## - KC 1 0.8 3962.7 -53150
## - DEN 1 0.8 3962.7 -53150
## - IND 1 0.8 3962.7 -53150
## - cold_weather 1 0.9 3962.8 -53149
## - MINN 1 1.1 3963.0 -53148
## - TB 1 1.1 3963.0 -53147
## - CLE 1 1.3 3963.2 -53146
## - HOU 1 1.3 3963.2 -53146
## - NOR 1 1.9 3963.8 -53142
## - NYG 1 2.4 3964.3 -53138
## - DAL 1 2.5 3964.4 -53138
## - avg_rbry_pos 1 3.1 3965.0 -53134
## - forty1 1 3.4 3965.3 -53132
## - SD 1 3.8 3965.7 -53129
## - vertical1 1 3.8 3965.7 -53129
## - avg_rectd_plyr 1 4.1 3966.0 -53127
## - NE 1 6.4 3968.3 -53111
## - GB 1 8.5 3970.4 -53096
## - weight 1 9.1 3971.0 -53092
## - avg_rbry_plyr 1 10.7 3972.6 -53081
## - height 1 17.4 3979.3 -53035
## - avg_fuml_plyr 1 79.8 4041.7 -52607
## - avg_qbtdp_plyr 1 7623.0 11584.9 -23665
##
## Step: AIC=-53154.92
## pc ~ height + weight + cold_weather + hot_weather + forty1 +
## vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.1 3962.0 -53156
## - hot_weather 1 0.1 3962.1 -53156
## - DET 1 0.2 3962.1 -53156
## - STL 1 0.2 3962.1 -53156
## - PIT 1 0.2 3962.2 -53155
## - CIN 1 0.3 3962.2 -53155
## <none> 3961.9 -53155
## - CAR 1 0.3 3962.2 -53155
## - OAK 1 0.3 3962.3 -53155
## - NYJ 1 0.4 3962.3 -53154
## - ATL 1 0.4 3962.3 -53154
## - TEN 1 0.5 3962.4 -53154
## - CHI 1 0.6 3962.6 -53153
## - WAS 1 0.7 3962.6 -53152
## - bad_weather_1 1 0.7 3962.7 -53152
## - PHI 1 0.8 3962.7 -53152
## - KC 1 0.8 3962.7 -53152
## - IND 1 0.8 3962.7 -53151
## - DEN 1 0.9 3962.8 -53151
## - cold_weather 1 1.0 3962.9 -53150
## - MINN 1 1.1 3963.1 -53149
## - TB 1 1.2 3963.1 -53149
## - CLE 1 1.2 3963.2 -53148
## - HOU 1 1.3 3963.3 -53148
## - NOR 1 1.8 3963.8 -53144
## - NYG 1 2.4 3964.3 -53140
## - DAL 1 2.4 3964.4 -53140
## - avg_rbry_pos 1 3.1 3965.1 -53135
## - forty1 1 3.4 3965.4 -53133
## - vertical1 1 3.8 3965.8 -53130
## - SD 1 3.9 3965.9 -53130
## - avg_rectd_plyr 1 4.1 3966.1 -53128
## - NE 1 6.4 3968.3 -53113
## - GB 1 8.6 3970.6 -53097
## - weight 1 9.1 3971.1 -53094
## - avg_rbry_plyr 1 10.8 3972.7 -53082
## - height 1 17.4 3979.3 -53037
## - avg_fuml_plyr 1 79.8 4041.7 -52609
## - avg_qbtdp_plyr 1 7623.0 11584.9 -23667
##
## Step: AIC=-53156.26
## pc ~ height + weight + cold_weather + hot_weather + forty1 +
## vertical1 + ATL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.1 3962.2 -53157
## - STL 1 0.2 3962.2 -53157
## - DET 1 0.2 3962.3 -53157
## - PIT 1 0.3 3962.3 -53156
## <none> 3962.0 -53156
## - CIN 1 0.3 3962.3 -53156
## - CAR 1 0.4 3962.4 -53156
## - OAK 1 0.4 3962.4 -53156
## - ATL 1 0.4 3962.5 -53155
## - NYJ 1 0.4 3962.5 -53155
## - TEN 1 0.5 3962.6 -53154
## - WAS 1 0.6 3962.6 -53154
## - PHI 1 0.7 3962.7 -53153
## - KC 1 0.7 3962.8 -53153
## - bad_weather_1 1 0.7 3962.8 -53153
## - CHI 1 0.7 3962.8 -53153
## - IND 1 0.9 3962.9 -53152
## - cold_weather 1 0.9 3963.0 -53152
## - DEN 1 1.0 3963.0 -53151
## - MINN 1 1.0 3963.1 -53151
## - CLE 1 1.2 3963.2 -53150
## - HOU 1 1.3 3963.3 -53149
## - TB 1 1.3 3963.3 -53149
## - NOR 1 2.0 3964.1 -53144
## - NYG 1 2.6 3964.6 -53140
## - DAL 1 2.6 3964.7 -53140
## - avg_rbry_pos 1 3.2 3965.2 -53136
## - forty1 1 3.4 3965.4 -53135
## - vertical1 1 3.9 3966.0 -53131
## - avg_rectd_plyr 1 4.1 3966.2 -53130
## - SD 1 4.2 3966.2 -53129
## - NE 1 6.7 3968.7 -53112
## - GB 1 9.1 3971.1 -53095
## - weight 1 9.2 3971.2 -53095
## - avg_rbry_plyr 1 10.8 3972.8 -53084
## - height 1 17.6 3979.6 -53037
## - avg_fuml_plyr 1 80.0 4042.0 -52609
## - avg_qbtdp_plyr 1 7628.2 11590.3 -23657
##
## Step: AIC=-53157.45
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND +
## KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - STL 1 0.2 3962.3 -53158
## - DET 1 0.2 3962.4 -53158
## - PIT 1 0.3 3962.4 -53157
## <none> 3962.2 -53157
## - CIN 1 0.3 3962.5 -53157
## - CAR 1 0.4 3962.5 -53157
## - OAK 1 0.4 3962.5 -53157
## - ATL 1 0.4 3962.6 -53156
## - NYJ 1 0.5 3962.6 -53156
## - TEN 1 0.5 3962.7 -53156
## - WAS 1 0.6 3962.8 -53155
## - CHI 1 0.7 3962.9 -53155
## - bad_weather_1 1 0.7 3962.9 -53155
## - PHI 1 0.7 3962.9 -53155
## - KC 1 0.7 3962.9 -53154
## - IND 1 0.9 3963.0 -53153
## - cold_weather 1 0.9 3963.1 -53153
## - DEN 1 1.0 3963.1 -53153
## - MINN 1 1.0 3963.2 -53152
## - CLE 1 1.2 3963.3 -53151
## - HOU 1 1.3 3963.4 -53151
## - TB 1 1.3 3963.5 -53150
## - NOR 1 2.0 3964.2 -53145
## - NYG 1 2.6 3964.7 -53142
## - DAL 1 2.6 3964.8 -53141
## - avg_rbry_pos 1 3.2 3965.3 -53137
## - forty1 1 3.4 3965.5 -53136
## - vertical1 1 3.9 3966.1 -53132
## - avg_rectd_plyr 1 4.1 3966.3 -53131
## - SD 1 4.3 3966.4 -53130
## - NE 1 6.7 3968.8 -53113
## - GB 1 9.1 3971.2 -53097
## - weight 1 9.2 3971.3 -53096
## - avg_rbry_plyr 1 10.8 3972.9 -53085
## - height 1 17.6 3979.7 -53038
## - avg_fuml_plyr 1 80.0 4042.1 -52610
## - avg_qbtdp_plyr 1 7628.5 11590.6 -23658
##
## Step: AIC=-53158.35
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND +
## KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DET 1 0.3 3962.6 -53159
## <none> 3962.3 -53158
## - PIT 1 0.3 3962.7 -53158
## - CIN 1 0.4 3962.7 -53158
## - CAR 1 0.4 3962.7 -53157
## - OAK 1 0.5 3962.8 -53157
## - ATL 1 0.5 3962.8 -53157
## - NYJ 1 0.5 3962.8 -53157
## - WAS 1 0.6 3962.9 -53157
## - TEN 1 0.6 3962.9 -53156
## - PHI 1 0.6 3963.0 -53156
## - KC 1 0.6 3963.0 -53156
## - bad_weather_1 1 0.7 3963.0 -53155
## - CHI 1 0.8 3963.1 -53155
## - cold_weather 1 0.9 3963.3 -53154
## - MINN 1 1.0 3963.3 -53154
## - IND 1 1.0 3963.3 -53153
## - CLE 1 1.1 3963.4 -53153
## - DEN 1 1.1 3963.4 -53153
## - HOU 1 1.2 3963.5 -53152
## - TB 1 1.5 3963.8 -53150
## - NOR 1 2.2 3964.5 -53145
## - NYG 1 2.8 3965.1 -53141
## - DAL 1 2.8 3965.1 -53141
## - avg_rbry_pos 1 3.2 3965.5 -53138
## - forty1 1 3.4 3965.7 -53137
## - vertical1 1 4.0 3966.3 -53133
## - avg_rectd_plyr 1 4.2 3966.5 -53131
## - SD 1 4.5 3966.9 -53129
## - NE 1 7.0 3969.3 -53112
## - weight 1 9.3 3971.6 -53096
## - GB 1 9.5 3971.8 -53095
## - avg_rbry_plyr 1 10.8 3973.1 -53085
## - height 1 17.6 3979.9 -53038
## - avg_fuml_plyr 1 80.2 4042.5 -52610
## - avg_qbtdp_plyr 1 7646.7 11609.0 -23616
##
## Step: AIC=-53158.56
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CAR + CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PIT 1 0.3 3962.9 -53159
## <none> 3962.6 -53159
## - CIN 1 0.3 3962.9 -53158
## - CAR 1 0.4 3962.9 -53158
## - OAK 1 0.4 3963.0 -53158
## - ATL 1 0.4 3963.0 -53158
## - NYJ 1 0.5 3963.0 -53157
## - TEN 1 0.6 3963.1 -53157
## - WAS 1 0.6 3963.2 -53156
## - CHI 1 0.7 3963.3 -53156
## - bad_weather_1 1 0.7 3963.3 -53155
## - PHI 1 0.7 3963.3 -53155
## - KC 1 0.7 3963.3 -53155
## - cold_weather 1 0.9 3963.5 -53154
## - IND 1 0.9 3963.5 -53154
## - DEN 1 1.0 3963.6 -53154
## - MINN 1 1.1 3963.7 -53153
## - CLE 1 1.2 3963.8 -53152
## - HOU 1 1.3 3963.9 -53151
## - TB 1 1.4 3963.9 -53151
## - NOR 1 2.0 3964.6 -53146
## - NYG 1 2.6 3965.2 -53142
## - DAL 1 2.7 3965.2 -53142
## - avg_rbry_pos 1 3.1 3965.7 -53139
## - forty1 1 3.4 3965.9 -53137
## - vertical1 1 4.1 3966.6 -53132
## - avg_rectd_plyr 1 4.3 3966.9 -53130
## - SD 1 4.4 3966.9 -53130
## - NE 1 6.8 3969.4 -53113
## - GB 1 9.3 3971.8 -53096
## - weight 1 9.3 3971.8 -53096
## - avg_rbry_plyr 1 10.7 3973.3 -53086
## - height 1 17.7 3980.2 -53038
## - avg_fuml_plyr 1 80.0 4042.6 -52611
## - avg_qbtdp_plyr 1 7646.5 11609.0 -23618
##
## Step: AIC=-53158.57
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CAR + CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CIN 1 0.3 3963.1 -53159
## <none> 3962.9 -53159
## - CAR 1 0.3 3963.2 -53159
## - OAK 1 0.3 3963.2 -53158
## - ATL 1 0.4 3963.2 -53158
## - NYJ 1 0.4 3963.2 -53158
## - TEN 1 0.5 3963.3 -53157
## - CHI 1 0.6 3963.5 -53156
## - WAS 1 0.7 3963.6 -53155
## - bad_weather_1 1 0.8 3963.6 -53155
## - IND 1 0.8 3963.7 -53155
## - PHI 1 0.8 3963.7 -53155
## - KC 1 0.9 3963.7 -53155
## - DEN 1 0.9 3963.8 -53154
## - cold_weather 1 1.0 3963.9 -53154
## - MINN 1 1.2 3964.1 -53152
## - TB 1 1.3 3964.1 -53152
## - CLE 1 1.4 3964.2 -53151
## - HOU 1 1.5 3964.3 -53150
## - NOR 1 1.9 3964.8 -53147
## - NYG 1 2.5 3965.3 -53143
## - DAL 1 2.5 3965.4 -53143
## - avg_rbry_pos 1 3.1 3965.9 -53139
## - forty1 1 3.4 3966.2 -53137
## - vertical1 1 4.1 3966.9 -53132
## - SD 1 4.2 3967.0 -53132
## - avg_rectd_plyr 1 4.4 3967.3 -53130
## - NE 1 6.6 3969.4 -53115
## - GB 1 9.0 3971.9 -53098
## - weight 1 9.2 3972.1 -53097
## - avg_rbry_plyr 1 10.7 3973.6 -53086
## - height 1 17.7 3980.5 -53038
## - avg_fuml_plyr 1 79.9 4042.7 -52612
## - avg_qbtdp_plyr 1 7646.4 11609.3 -23620
##
## Step: AIC=-53158.83
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CAR + CHI + CLE + DAL + DEN + GB + HOU + IND + KC + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CAR 1 0.2 3963.4 -53159
## - OAK 1 0.3 3963.4 -53159
## <none> 3963.1 -53159
## - ATL 1 0.3 3963.4 -53159
## - NYJ 1 0.3 3963.4 -53159
## - TEN 1 0.4 3963.5 -53158
## - CHI 1 0.6 3963.7 -53157
## - IND 1 0.7 3963.8 -53156
## - bad_weather_1 1 0.8 3963.9 -53156
## - DEN 1 0.8 3963.9 -53155
## - WAS 1 0.8 3963.9 -53155
## - PHI 1 0.9 3964.0 -53154
## - KC 1 1.0 3964.1 -53154
## - cold_weather 1 1.0 3964.2 -53154
## - TB 1 1.2 3964.3 -53153
## - MINN 1 1.3 3964.4 -53152
## - CLE 1 1.5 3964.6 -53151
## - HOU 1 1.6 3964.7 -53150
## - NOR 1 1.8 3964.9 -53148
## - NYG 1 2.3 3965.5 -53145
## - DAL 1 2.4 3965.5 -53144
## - avg_rbry_pos 1 3.1 3966.2 -53139
## - forty1 1 3.3 3966.4 -53138
## - SD 1 4.0 3967.1 -53133
## - vertical1 1 4.0 3967.2 -53133
## - avg_rectd_plyr 1 4.4 3967.5 -53130
## - NE 1 6.4 3969.5 -53117
## - GB 1 8.8 3971.9 -53100
## - weight 1 9.1 3972.2 -53098
## - avg_rbry_plyr 1 10.8 3973.9 -53086
## - height 1 17.5 3980.7 -53039
## - avg_fuml_plyr 1 79.9 4043.1 -52612
## - avg_qbtdp_plyr 1 7648.3 11611.4 -23617
##
## Step: AIC=-53159.09
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CHI + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.2 3963.6 -53159
## - ATL 1 0.3 3963.6 -53159
## <none> 3963.4 -53159
## - NYJ 1 0.3 3963.6 -53159
## - TEN 1 0.4 3963.7 -53159
## - CHI 1 0.5 3963.9 -53158
## - IND 1 0.7 3964.0 -53156
## - DEN 1 0.7 3964.1 -53156
## - bad_weather_1 1 0.8 3964.1 -53156
## - WAS 1 0.9 3964.3 -53155
## - PHI 1 1.0 3964.4 -53154
## - cold_weather 1 1.0 3964.4 -53154
## - KC 1 1.0 3964.4 -53154
## - TB 1 1.1 3964.4 -53154
## - MINN 1 1.4 3964.8 -53151
## - CLE 1 1.6 3964.9 -53150
## - NOR 1 1.7 3965.1 -53149
## - HOU 1 1.7 3965.1 -53149
## - NYG 1 2.2 3965.6 -53146
## - DAL 1 2.3 3965.6 -53145
## - avg_rbry_pos 1 3.2 3966.5 -53139
## - forty1 1 3.4 3966.7 -53138
## - SD 1 3.9 3967.3 -53134
## - vertical1 1 4.1 3967.4 -53133
## - avg_rectd_plyr 1 4.4 3967.7 -53131
## - NE 1 6.2 3969.6 -53118
## - GB 1 8.6 3972.0 -53101
## - weight 1 9.3 3972.6 -53097
## - avg_rbry_plyr 1 10.9 3974.3 -53086
## - height 1 17.7 3981.0 -53039
## - avg_fuml_plyr 1 79.9 4043.3 -52612
## - avg_qbtdp_plyr 1 7649.1 11612.4 -23616
##
## Step: AIC=-53159.45
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL +
## CHI + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE +
## NOR + NYG + NYJ + PHI + SD + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ATL 1 0.2 3963.8 -53160
## - NYJ 1 0.3 3963.9 -53160
## <none> 3963.6 -53159
## - TEN 1 0.3 3963.9 -53159
## - CHI 1 0.5 3964.1 -53158
## - IND 1 0.6 3964.2 -53157
## - DEN 1 0.7 3964.3 -53157
## - bad_weather_1 1 0.8 3964.4 -53156
## - cold_weather 1 1.0 3964.6 -53155
## - WAS 1 1.0 3964.6 -53155
## - TB 1 1.0 3964.6 -53154
## - PHI 1 1.1 3964.7 -53154
## - KC 1 1.1 3964.7 -53154
## - MINN 1 1.5 3965.1 -53151
## - NOR 1 1.6 3965.2 -53150
## - CLE 1 1.7 3965.3 -53150
## - HOU 1 1.8 3965.4 -53149
## - NYG 1 2.1 3965.7 -53147
## - DAL 1 2.2 3965.8 -53146
## - avg_rbry_pos 1 3.1 3966.7 -53140
## - forty1 1 3.5 3967.1 -53137
## - SD 1 3.8 3967.4 -53135
## - vertical1 1 4.0 3967.6 -53134
## - avg_rectd_plyr 1 4.3 3967.9 -53132
## - NE 1 6.1 3969.7 -53119
## - GB 1 8.5 3972.0 -53103
## - weight 1 9.2 3972.8 -53098
## - avg_rbry_plyr 1 10.8 3974.4 -53086
## - height 1 17.5 3981.1 -53041
## - avg_fuml_plyr 1 80.2 4043.8 -52611
## - avg_qbtdp_plyr 1 7648.9 11612.5 -23618
##
## Step: AIC=-53159.75
## pc ~ height + weight + cold_weather + forty1 + vertical1 + CHI +
## CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + NOR +
## NYG + NYJ + PHI + SD + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NYJ 1 0.2 3964.1 -53160
## <none> 3963.8 -53160
## - TEN 1 0.3 3964.1 -53160
## - CHI 1 0.4 3964.3 -53159
## - IND 1 0.6 3964.4 -53158
## - DEN 1 0.6 3964.5 -53157
## - bad_weather_1 1 0.8 3964.6 -53156
## - cold_weather 1 0.9 3964.8 -53155
## - TB 1 0.9 3964.8 -53155
## - WAS 1 1.1 3964.9 -53154
## - PHI 1 1.2 3965.0 -53154
## - KC 1 1.2 3965.1 -53153
## - NOR 1 1.5 3965.4 -53151
## - MINN 1 1.6 3965.5 -53151
## - CLE 1 1.8 3965.6 -53149
## - HOU 1 2.0 3965.8 -53148
## - NYG 1 2.0 3965.9 -53148
## - DAL 1 2.1 3965.9 -53147
## - avg_rbry_pos 1 3.1 3966.9 -53141
## - forty1 1 3.5 3967.3 -53138
## - SD 1 3.7 3967.5 -53136
## - vertical1 1 3.9 3967.8 -53135
## - avg_rectd_plyr 1 4.5 3968.3 -53131
## - NE 1 5.9 3969.8 -53121
## - GB 1 8.3 3972.1 -53104
## - weight 1 9.2 3973.0 -53098
## - avg_rbry_plyr 1 10.9 3974.7 -53087
## - height 1 17.7 3981.5 -53040
## - avg_fuml_plyr 1 80.7 4044.6 -52607
## - avg_qbtdp_plyr 1 7659.4 11623.2 -23595
##
## Step: AIC=-53160.2
## pc ~ height + weight + cold_weather + forty1 + vertical1 + CHI +
## CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + NOR +
## NYG + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TEN 1 0.3 3964.3 -53160
## <none> 3964.1 -53160
## - CHI 1 0.4 3964.5 -53160
## - IND 1 0.5 3964.6 -53159
## - DEN 1 0.6 3964.6 -53158
## - bad_weather_1 1 0.8 3964.8 -53157
## - TB 1 0.9 3965.0 -53156
## - cold_weather 1 1.0 3965.0 -53156
## - WAS 1 1.1 3965.2 -53154
## - PHI 1 1.3 3965.3 -53154
## - KC 1 1.3 3965.4 -53153
## - NOR 1 1.4 3965.5 -53152
## - MINN 1 1.7 3965.8 -53150
## - CLE 1 1.9 3965.9 -53149
## - NYG 1 2.0 3966.0 -53149
## - DAL 1 2.0 3966.1 -53148
## - HOU 1 2.1 3966.1 -53148
## - avg_rbry_pos 1 3.1 3967.2 -53141
## - forty1 1 3.4 3967.5 -53139
## - SD 1 3.6 3967.6 -53138
## - vertical1 1 4.1 3968.1 -53134
## - avg_rectd_plyr 1 4.4 3968.5 -53131
## - NE 1 5.8 3969.9 -53122
## - GB 1 8.1 3972.2 -53106
## - weight 1 9.2 3973.2 -53099
## - avg_rbry_plyr 1 10.9 3975.0 -53087
## - height 1 17.7 3981.7 -53040
## - avg_fuml_plyr 1 80.5 4044.6 -52609
## - avg_qbtdp_plyr 1 7669.1 11633.2 -23573
##
## Step: AIC=-53160.4
## pc ~ height + weight + cold_weather + forty1 + vertical1 + CHI +
## CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + NOR +
## NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## <none> 3964.3 -53160
## - CHI 1 0.4 3964.7 -53160
## - IND 1 0.5 3964.8 -53159
## - DEN 1 0.5 3964.9 -53159
## - bad_weather_1 1 0.7 3965.1 -53157
## - TB 1 0.8 3965.2 -53157
## - cold_weather 1 0.9 3965.3 -53156
## - WAS 1 1.2 3965.5 -53154
## - PHI 1 1.3 3965.7 -53153
## - KC 1 1.4 3965.7 -53153
## - NOR 1 1.4 3965.7 -53153
## - MINN 1 1.8 3966.1 -53150
## - NYG 1 1.9 3966.2 -53149
## - DAL 1 1.9 3966.2 -53149
## - CLE 1 2.0 3966.3 -53149
## - HOU 1 2.2 3966.5 -53147
## - avg_rbry_pos 1 3.1 3967.4 -53141
## - forty1 1 3.4 3967.7 -53139
## - SD 1 3.5 3967.8 -53138
## - vertical1 1 4.1 3968.4 -53134
## - avg_rectd_plyr 1 4.4 3968.7 -53132
## - NE 1 5.7 3970.0 -53123
## - GB 1 8.0 3972.3 -53107
## - weight 1 9.1 3973.5 -53099
## - avg_rbry_plyr 1 10.9 3975.2 -53087
## - height 1 17.6 3981.9 -53041
## - avg_fuml_plyr 1 80.4 4044.7 -52611
## - avg_qbtdp_plyr 1 7679.4 11643.7 -23550Ints
PreProcess:
set.seed(123)
splitints <- sample.split(nfl_data$ints, SplitRatio = 0.7)
Trainints <- subset(nfl_data, split == TRUE)
Testints <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainints, method = c("center", "scale"))
trainTransformedints <- predict(preProcValues, Trainints)
testTransformedints <- predict(preProcValues, Testints)ggpairs:
ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[46:51]))])
intsregform <- formula(paste("ints ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegQBInts <- lm(intsregform, data = trainTransformedints)
summary(linRegQBInts) ##
## Call:
## lm(formula = intsregform, data = trainTransformedints)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8765 -0.0764 -0.0179 0.0449 10.8466
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.022e-15 4.798e-03 0.000 1.000000
## height 5.147e-02 9.310e-03 5.529 3.26e-08 ***
## weight -3.398e-02 8.725e-03 -3.894 9.88e-05 ***
## cold_weather 6.206e-03 5.051e-03 1.229 0.219163
## hot_weather 1.959e-03 4.842e-03 0.404 0.685865
## home_team_1 -6.020e-03 5.221e-03 -1.153 0.248898
## forty1 3.365e-02 8.281e-03 4.063 4.85e-05 ***
## vertical1 -9.503e-03 6.367e-03 -1.493 0.135573
## ARI 1.016e-02 6.712e-03 1.513 0.130288
## ATL -5.294e-03 6.744e-03 -0.785 0.432456
## BAL 7.636e-03 6.750e-03 1.131 0.257943
## BUF 8.200e-03 6.663e-03 1.231 0.218466
## CAR 1.264e-02 6.620e-03 1.909 0.056221 .
## CHI 1.153e-03 6.546e-03 0.176 0.860172
## CIN 4.949e-03 6.667e-03 0.742 0.457881
## CLE 1.330e-02 6.636e-03 2.004 0.045115 *
## DAL -4.229e-03 6.703e-03 -0.631 0.528103
## DEN -1.841e-03 6.728e-03 -0.274 0.784340
## DET -2.741e-03 6.636e-03 -0.413 0.679585
## GB -1.826e-02 6.832e-03 -2.672 0.007535 **
## HOU 9.650e-03 6.750e-03 1.430 0.152830
## IND 5.421e-03 6.701e-03 0.809 0.418550
## JAC 1.531e-02 6.537e-03 2.343 0.019147 *
## KC 4.489e-04 6.680e-03 0.067 0.946424
## MIA 2.154e-03 6.572e-03 0.328 0.743135
## MINN 1.064e-02 6.613e-03 1.609 0.107730
## NE -2.341e-02 6.906e-03 -3.389 0.000701 ***
## NOR -3.791e-03 6.885e-03 -0.551 0.581846
## NYG 6.865e-04 6.729e-03 0.102 0.918749
## NYJ 1.076e-02 6.704e-03 1.604 0.108674
## OAK 1.077e-02 6.747e-03 1.597 0.110373
## PHI 1.066e-02 6.538e-03 1.630 0.103015
## PIT -5.227e-03 6.709e-03 -0.779 0.435978
## SD -6.953e-03 6.584e-03 -1.056 0.290971
## SEA 2.720e-03 6.833e-03 0.398 0.690581
## STL 3.603e-03 6.651e-03 0.542 0.588043
## TB 1.134e-03 6.588e-03 0.172 0.863375
## TEN 5.676e-04 6.628e-03 0.086 0.931758
## WAS 9.808e-03 6.663e-03 1.472 0.141046
## avg_trg_team NA NA NA NA
## avg_rectd_plyr -2.067e-02 6.127e-03 -3.373 0.000743 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr -5.063e-02 7.333e-03 -6.905 5.12e-12 ***
## avg_rbry_pos 2.058e-02 8.544e-03 2.409 0.016011 *
## avg_fuml_plyr 1.376e-01 7.088e-03 19.418 < 2e-16 ***
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr 4.727e-01 7.699e-03 61.396 < 2e-16 ***
## avg_qbtdp_team NA NA NA NA
## grass_1 5.163e-04 5.521e-03 0.094 0.925497
## bad_weather_1 8.351e-03 4.881e-03 1.711 0.087131 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7955 on 27438 degrees of freedom
## Multiple R-squared: 0.3682, Adjusted R-squared: 0.3672
## F-statistic: 355.4 on 45 and 27438 DF, p-value: < 2.2e-16linRegQBInts2 <- lm(ints ~ avg_qbints_plyr, data = trainTransformedints)
summary(linRegQBInts2)##
## Call:
## lm(formula = ints ~ avg_qbints_plyr, data = trainTransformedints)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0750 -0.0018 -0.0018 -0.0018 11.2261
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.104e-15 4.606e-03 0.0 1
## avg_qbints_plyr 6.457e-01 4.606e-03 140.2 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7636 on 27482 degrees of freedom
## Multiple R-squared: 0.417, Adjusted R-squared: 0.4169
## F-statistic: 1.965e+04 on 1 and 27482 DF, p-value: < 2.2e-16R2 of 0.4169, and really the only meaningful predictor was “how many interceptions have you thrown in the past”. Not an entirely amazing model, but at least we have something here.
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
PintPredicted <- predict(linRegQBInts2, newdata = testTransformedints)
SSEint <- sum((PintPredicted - testTransformedints$ints)^2)
SSTint <- sum((mean(nfl_data$ints)-testTransformedints$ints)^2)
r2_int <- 1 - SSEint/SSTint
r2_int## [1] 0.4500887rmse_int <- sqrt(SSEint/nrow(testTransformedints))
rmse_int## [1] 0.7879945Regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBInts2, which = c(1:3,5))
Summary statistics:
confint(linRegQBInts2)## 2.5 % 97.5 %
## (Intercept) -0.009027885 0.009027885
## avg_qbints_plyr 0.636692876 0.654748974coef(summary(linRegQBInts2))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.104007e-15 0.004605945 -4.568024e-13 1
## avg_qbints_plyr 6.457209e-01 0.004606029 1.401904e+02 0anova(linRegQBInts2)## Analysis of Variance Table
##
## Response: ints
## Df Sum Sq Mean Sq F value Pr(>F)
## avg_qbints_plyr 1 11459 11459.2 19653 < 2.2e-16 ***
## Residuals 27482 16024 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_ints <- step(lm(intsregform, data = trainTransformedints), direction = "backward")## Start: AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - KC 1 0.00 17363 -12532.9
## - TEN 1 0.00 17363 -12532.9
## - grass_1 1 0.01 17363 -12532.9
## - NYG 1 0.01 17363 -12532.9
## - TB 1 0.02 17363 -12532.9
## - CHI 1 0.02 17363 -12532.9
## - DEN 1 0.05 17363 -12532.8
## - MIA 1 0.07 17363 -12532.8
## - SEA 1 0.10 17363 -12532.8
## - hot_weather 1 0.10 17363 -12532.8
## - DET 1 0.11 17363 -12532.7
## - STL 1 0.19 17363 -12532.6
## - NOR 1 0.19 17363 -12532.6
## - DAL 1 0.25 17363 -12532.5
## - CIN 1 0.35 17363 -12532.4
## - PIT 1 0.38 17363 -12532.3
## - ATL 1 0.39 17363 -12532.3
## - IND 1 0.41 17363 -12532.3
## - SD 1 0.71 17363 -12531.8
## - BAL 1 0.81 17364 -12531.6
## - home_team_1 1 0.84 17364 -12531.6
## - cold_weather 1 0.96 17364 -12531.4
## - BUF 1 0.96 17364 -12531.4
## <none> 17363 -12530.9
## - HOU 1 1.29 17364 -12530.9
## - WAS 1 1.37 17364 -12530.7
## - vertical1 1 1.41 17364 -12530.7
## - ARI 1 1.45 17364 -12530.6
## - OAK 1 1.61 17364 -12530.4
## - NYJ 1 1.63 17364 -12530.3
## - MINN 1 1.64 17364 -12530.3
## - PHI 1 1.68 17364 -12530.3
## - bad_weather_1 1 1.85 17365 -12530.0
## - CAR 1 2.31 17365 -12529.3
## - CLE 1 2.54 17365 -12528.9
## - JAC 1 3.47 17366 -12527.4
## - avg_rbry_pos 1 3.67 17366 -12527.1
## - GB 1 4.52 17367 -12525.8
## - avg_rectd_plyr 1 7.20 17370 -12521.5
## - NE 1 7.27 17370 -12521.4
## - weight 1 9.60 17372 -12517.7
## - forty1 1 10.45 17373 -12516.4
## - height 1 19.34 17382 -12502.3
## - avg_rbry_plyr 1 30.17 17393 -12485.2
## - avg_fuml_plyr 1 238.61 17601 -12157.8
## - avg_qbtdp_plyr 1 2385.32 19748 -8994.9
##
## Step: AIC=-12532.91
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TEN 1 0.00 17363 -12534.9
## - NYG 1 0.00 17363 -12534.9
## - grass_1 1 0.01 17363 -12534.9
## - TB 1 0.02 17363 -12534.9
## - CHI 1 0.02 17363 -12534.9
## - MIA 1 0.07 17363 -12534.8
## - DEN 1 0.08 17363 -12534.8
## - hot_weather 1 0.10 17363 -12534.7
## - SEA 1 0.11 17363 -12534.7
## - DET 1 0.16 17363 -12534.7
## - STL 1 0.21 17363 -12534.6
## - NOR 1 0.29 17363 -12534.5
## - DAL 1 0.36 17363 -12534.3
## - CIN 1 0.42 17363 -12534.3
## - IND 1 0.50 17363 -12534.1
## - ATL 1 0.55 17363 -12534.0
## - PIT 1 0.56 17363 -12534.0
## - home_team_1 1 0.84 17364 -12533.6
## - cold_weather 1 0.96 17364 -12533.4
## - SD 1 0.98 17364 -12533.4
## - BAL 1 1.01 17364 -12533.3
## - BUF 1 1.19 17364 -12533.0
## <none> 17363 -12532.9
## - vertical1 1 1.41 17364 -12532.7
## - HOU 1 1.62 17364 -12532.4
## - WAS 1 1.74 17364 -12532.2
## - ARI 1 1.81 17365 -12532.0
## - bad_weather_1 1 1.85 17365 -12532.0
## - MINN 1 2.05 17365 -12531.7
## - NYJ 1 2.05 17365 -12531.7
## - OAK 1 2.06 17365 -12531.6
## - PHI 1 2.11 17365 -12531.6
## - CAR 1 2.94 17366 -12530.3
## - CLE 1 3.25 17366 -12529.8
## - avg_rbry_pos 1 3.68 17366 -12529.1
## - JAC 1 4.41 17367 -12527.9
## - GB 1 6.21 17369 -12525.1
## - avg_rectd_plyr 1 7.22 17370 -12523.5
## - weight 1 9.61 17372 -12519.7
## - NE 1 9.72 17372 -12519.5
## - forty1 1 10.45 17373 -12518.4
## - height 1 19.38 17382 -12504.3
## - avg_rbry_plyr 1 30.18 17393 -12487.2
## - avg_fuml_plyr 1 238.62 17601 -12159.8
## - avg_qbtdp_plyr 1 2386.52 19749 -8995.3
##
## Step: AIC=-12534.91
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NYG 1 0.00 17363 -12536.9
## - grass_1 1 0.01 17363 -12536.9
## - TB 1 0.01 17363 -12536.9
## - CHI 1 0.01 17363 -12536.9
## - MIA 1 0.07 17363 -12536.8
## - DEN 1 0.10 17363 -12536.8
## - hot_weather 1 0.10 17363 -12536.7
## - SEA 1 0.11 17363 -12536.7
## - DET 1 0.19 17363 -12536.6
## - STL 1 0.22 17363 -12536.6
## - NOR 1 0.34 17363 -12536.4
## - DAL 1 0.42 17363 -12536.2
## - CIN 1 0.44 17363 -12536.2
## - IND 1 0.53 17363 -12536.1
## - ATL 1 0.64 17363 -12535.9
## - PIT 1 0.65 17363 -12535.9
## - home_team_1 1 0.84 17364 -12535.6
## - cold_weather 1 0.96 17364 -12535.4
## - BAL 1 1.10 17364 -12535.2
## - SD 1 1.13 17364 -12535.1
## <none> 17363 -12534.9
## - BUF 1 1.28 17364 -12534.9
## - vertical1 1 1.41 17364 -12534.7
## - HOU 1 1.76 17364 -12534.1
## - bad_weather_1 1 1.85 17365 -12534.0
## - WAS 1 1.90 17365 -12533.9
## - ARI 1 1.97 17365 -12533.8
## - MINN 1 2.23 17365 -12533.4
## - NYJ 1 2.24 17365 -12533.4
## - OAK 1 2.27 17365 -12533.3
## - PHI 1 2.30 17365 -12533.3
## - CAR 1 3.23 17366 -12531.8
## - CLE 1 3.57 17366 -12531.3
## - avg_rbry_pos 1 3.68 17366 -12531.1
## - JAC 1 4.84 17368 -12529.3
## - GB 1 7.05 17370 -12525.8
## - avg_rectd_plyr 1 7.23 17370 -12525.5
## - weight 1 9.63 17372 -12521.7
## - forty1 1 10.45 17373 -12520.4
## - NE 1 10.92 17374 -12519.6
## - height 1 19.39 17382 -12506.2
## - avg_rbry_plyr 1 30.20 17393 -12489.1
## - avg_fuml_plyr 1 238.82 17602 -12161.5
## - avg_qbtdp_plyr 1 2387.65 19750 -8995.7
##
## Step: AIC=-12536.91
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 0.00 17363 -12538.9
## - TB 1 0.01 17363 -12538.9
## - CHI 1 0.01 17363 -12538.9
## - MIA 1 0.07 17363 -12538.8
## - hot_weather 1 0.10 17363 -12538.7
## - SEA 1 0.11 17363 -12538.7
## - DEN 1 0.12 17363 -12538.7
## - DET 1 0.22 17363 -12538.6
## - STL 1 0.22 17363 -12538.6
## - NOR 1 0.39 17363 -12538.3
## - CIN 1 0.46 17363 -12538.2
## - DAL 1 0.47 17363 -12538.2
## - IND 1 0.55 17363 -12538.0
## - ATL 1 0.71 17363 -12537.8
## - PIT 1 0.72 17363 -12537.8
## - home_team_1 1 0.84 17364 -12537.6
## - cold_weather 1 0.97 17364 -12537.4
## - BAL 1 1.16 17364 -12537.1
## - SD 1 1.23 17364 -12537.0
## <none> 17363 -12536.9
## - BUF 1 1.35 17364 -12536.8
## - vertical1 1 1.41 17364 -12536.7
## - HOU 1 1.85 17365 -12536.0
## - bad_weather_1 1 1.85 17365 -12536.0
## - WAS 1 1.98 17365 -12535.8
## - ARI 1 2.08 17365 -12535.6
## - MINN 1 2.35 17365 -12535.2
## - NYJ 1 2.37 17365 -12535.2
## - OAK 1 2.37 17365 -12535.2
## - PHI 1 2.41 17365 -12535.1
## - CAR 1 3.39 17366 -12533.5
## - avg_rbry_pos 1 3.69 17366 -12533.1
## - CLE 1 3.75 17366 -12533.0
## - JAC 1 5.07 17368 -12530.9
## - avg_rectd_plyr 1 7.23 17370 -12527.5
## - GB 1 7.66 17370 -12526.8
## - weight 1 9.63 17372 -12523.7
## - forty1 1 10.46 17373 -12522.4
## - NE 1 12.00 17375 -12519.9
## - height 1 19.40 17382 -12508.2
## - avg_rbry_plyr 1 30.22 17393 -12491.1
## - avg_fuml_plyr 1 238.82 17602 -12163.4
## - avg_qbtdp_plyr 1 2387.80 19751 -8997.5
##
## Step: AIC=-12538.9
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TB 1 0.01 17363 -12540.9
## - CHI 1 0.01 17363 -12540.9
## - MIA 1 0.07 17363 -12540.8
## - hot_weather 1 0.11 17363 -12540.7
## - SEA 1 0.11 17363 -12540.7
## - DEN 1 0.11 17363 -12540.7
## - STL 1 0.22 17363 -12540.5
## - DET 1 0.23 17363 -12540.5
## - NOR 1 0.40 17363 -12540.3
## - CIN 1 0.45 17363 -12540.2
## - DAL 1 0.49 17363 -12540.1
## - IND 1 0.54 17363 -12540.0
## - PIT 1 0.71 17363 -12539.8
## - ATL 1 0.72 17363 -12539.8
## - home_team_1 1 0.84 17364 -12539.6
## - cold_weather 1 0.98 17364 -12539.3
## - BAL 1 1.15 17364 -12539.1
## - SD 1 1.22 17364 -12539.0
## <none> 17363 -12538.9
## - BUF 1 1.35 17364 -12538.8
## - vertical1 1 1.41 17364 -12538.7
## - HOU 1 1.85 17365 -12538.0
## - bad_weather_1 1 1.86 17365 -12538.0
## - WAS 1 1.99 17365 -12537.7
## - ARI 1 2.08 17365 -12537.6
## - MINN 1 2.36 17365 -12537.2
## - NYJ 1 2.38 17365 -12537.1
## - OAK 1 2.40 17365 -12537.1
## - PHI 1 2.42 17365 -12537.1
## - CAR 1 3.40 17366 -12535.5
## - avg_rbry_pos 1 3.69 17366 -12535.1
## - CLE 1 3.77 17366 -12534.9
## - JAC 1 5.09 17368 -12532.8
## - avg_rectd_plyr 1 7.24 17370 -12529.4
## - GB 1 7.65 17370 -12528.8
## - weight 1 9.63 17372 -12525.7
## - forty1 1 10.46 17373 -12524.3
## - NE 1 12.31 17375 -12521.4
## - height 1 19.40 17382 -12510.2
## - avg_rbry_plyr 1 30.22 17393 -12493.1
## - avg_fuml_plyr 1 238.82 17602 -12165.4
## - avg_qbtdp_plyr 1 2387.94 19751 -8999.3
##
## Step: AIC=-12540.88
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CHI 1 0.01 17363 -12542.9
## - MIA 1 0.06 17363 -12542.8
## - SEA 1 0.10 17363 -12542.7
## - hot_weather 1 0.11 17363 -12542.7
## - DEN 1 0.13 17363 -12542.7
## - STL 1 0.21 17363 -12542.5
## - DET 1 0.26 17363 -12542.5
## - CIN 1 0.44 17363 -12542.2
## - NOR 1 0.45 17363 -12542.2
## - IND 1 0.53 17363 -12542.0
## - DAL 1 0.54 17363 -12542.0
## - PIT 1 0.78 17364 -12541.6
## - ATL 1 0.79 17364 -12541.6
## - home_team_1 1 0.84 17364 -12541.6
## - cold_weather 1 0.97 17364 -12541.3
## - BAL 1 1.15 17364 -12541.1
## <none> 17363 -12540.9
## - SD 1 1.32 17364 -12540.8
## - BUF 1 1.35 17364 -12540.7
## - vertical1 1 1.42 17364 -12540.6
## - bad_weather_1 1 1.86 17365 -12539.9
## - HOU 1 1.86 17365 -12539.9
## - WAS 1 2.01 17365 -12539.7
## - ARI 1 2.10 17365 -12539.6
## - MINN 1 2.38 17365 -12539.1
## - NYJ 1 2.41 17365 -12539.1
## - OAK 1 2.43 17365 -12539.0
## - PHI 1 2.44 17365 -12539.0
## - CAR 1 3.45 17366 -12537.4
## - avg_rbry_pos 1 3.69 17366 -12537.0
## - CLE 1 3.82 17367 -12536.8
## - JAC 1 5.18 17368 -12534.7
## - avg_rectd_plyr 1 7.24 17370 -12531.4
## - GB 1 8.08 17371 -12530.1
## - weight 1 9.62 17372 -12527.7
## - forty1 1 10.45 17373 -12526.3
## - NE 1 12.93 17376 -12522.4
## - height 1 19.40 17382 -12512.2
## - avg_rbry_plyr 1 30.23 17393 -12495.1
## - avg_fuml_plyr 1 238.88 17602 -12167.3
## - avg_qbtdp_plyr 1 2387.94 19751 -9001.2
##
## Step: AIC=-12542.86
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN +
## NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.06 17363 -12545
## - SEA 1 0.09 17363 -12545
## - hot_weather 1 0.11 17363 -12545
## - DEN 1 0.15 17363 -12545
## - STL 1 0.20 17363 -12544
## - DET 1 0.28 17363 -12544
## - CIN 1 0.43 17363 -12544
## - NOR 1 0.48 17363 -12544
## - IND 1 0.52 17363 -12544
## - DAL 1 0.58 17363 -12544
## - PIT 1 0.83 17364 -12544
## - ATL 1 0.84 17364 -12544
## - home_team_1 1 0.84 17364 -12544
## - cold_weather 1 0.98 17364 -12543
## - BAL 1 1.15 17364 -12543
## <none> 17363 -12543
## - BUF 1 1.35 17364 -12543
## - SD 1 1.39 17364 -12543
## - vertical1 1 1.43 17364 -12543
## - bad_weather_1 1 1.87 17365 -12542
## - HOU 1 1.87 17365 -12542
## - WAS 1 2.01 17365 -12542
## - ARI 1 2.11 17365 -12542
## - MINN 1 2.39 17365 -12541
## - NYJ 1 2.42 17365 -12541
## - OAK 1 2.44 17365 -12541
## - PHI 1 2.45 17365 -12541
## - CAR 1 3.48 17366 -12539
## - avg_rbry_pos 1 3.69 17366 -12539
## - CLE 1 3.86 17367 -12539
## - JAC 1 5.23 17368 -12537
## - avg_rectd_plyr 1 7.24 17370 -12533
## - GB 1 8.41 17371 -12532
## - weight 1 9.65 17372 -12530
## - forty1 1 10.44 17373 -12528
## - NE 1 13.38 17376 -12524
## - height 1 19.48 17382 -12514
## - avg_rbry_plyr 1 30.23 17393 -12497
## - avg_fuml_plyr 1 239.10 17602 -12169
## - avg_qbtdp_plyr 1 2388.79 19752 -9002
##
## Step: AIC=-12544.78
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE +
## NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.07 17363 -12546.7
## - hot_weather 1 0.11 17363 -12546.6
## - STL 1 0.18 17363 -12546.5
## - DEN 1 0.18 17363 -12546.5
## - DET 1 0.32 17363 -12546.3
## - CIN 1 0.40 17363 -12546.1
## - IND 1 0.49 17363 -12546.0
## - NOR 1 0.54 17363 -12545.9
## - DAL 1 0.64 17363 -12545.8
## - home_team_1 1 0.84 17364 -12545.4
## - PIT 1 0.91 17364 -12545.3
## - ATL 1 0.92 17364 -12545.3
## - cold_weather 1 0.97 17364 -12545.2
## - BAL 1 1.10 17364 -12545.0
## <none> 17363 -12544.8
## - BUF 1 1.30 17364 -12544.7
## - vertical1 1 1.44 17364 -12544.5
## - SD 1 1.49 17364 -12544.4
## - HOU 1 1.82 17365 -12543.9
## - bad_weather_1 1 1.86 17365 -12543.8
## - WAS 1 1.96 17365 -12543.7
## - ARI 1 2.05 17365 -12543.5
## - MINN 1 2.33 17365 -12543.1
## - NYJ 1 2.37 17365 -12543.0
## - OAK 1 2.39 17365 -12543.0
## - PHI 1 2.40 17365 -12543.0
## - CAR 1 3.43 17366 -12541.3
## - avg_rbry_pos 1 3.71 17367 -12540.9
## - CLE 1 3.81 17367 -12540.8
## - JAC 1 5.18 17368 -12538.6
## - avg_rectd_plyr 1 7.22 17370 -12535.4
## - GB 1 8.80 17372 -12532.9
## - weight 1 9.65 17372 -12531.5
## - forty1 1 10.43 17373 -12530.3
## - NE 1 13.92 17377 -12524.7
## - height 1 19.47 17382 -12516.0
## - avg_rbry_plyr 1 30.29 17393 -12498.9
## - avg_fuml_plyr 1 239.12 17602 -12170.8
## - avg_qbtdp_plyr 1 2388.80 19752 -9003.9
##
## Step: AIC=-12546.66
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE +
## NOR + NYJ + OAK + PHI + PIT + SD + STL + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.12 17363 -12548.5
## - STL 1 0.15 17363 -12548.4
## - DEN 1 0.22 17363 -12548.3
## - CIN 1 0.36 17363 -12548.1
## - DET 1 0.37 17363 -12548.1
## - IND 1 0.45 17363 -12548.0
## - NOR 1 0.61 17363 -12547.7
## - DAL 1 0.71 17364 -12547.5
## - home_team_1 1 0.84 17364 -12547.3
## - PIT 1 1.00 17364 -12547.1
## - cold_weather 1 1.00 17364 -12547.1
## - ATL 1 1.00 17364 -12547.1
## - BAL 1 1.04 17364 -12547.0
## - BUF 1 1.24 17364 -12546.7
## <none> 17363 -12546.7
## - vertical1 1 1.43 17364 -12546.4
## - SD 1 1.60 17364 -12546.1
## - HOU 1 1.75 17365 -12545.9
## - bad_weather_1 1 1.86 17365 -12545.7
## - WAS 1 1.89 17365 -12545.7
## - ARI 1 1.99 17365 -12545.5
## - MINN 1 2.27 17365 -12545.1
## - NYJ 1 2.30 17365 -12545.0
## - OAK 1 2.32 17365 -12545.0
## - PHI 1 2.33 17365 -12545.0
## - CAR 1 3.36 17366 -12543.3
## - avg_rbry_pos 1 3.68 17367 -12542.8
## - CLE 1 3.73 17367 -12542.8
## - JAC 1 5.11 17368 -12540.6
## - avg_rectd_plyr 1 7.20 17370 -12537.3
## - GB 1 9.22 17372 -12534.1
## - weight 1 9.61 17372 -12533.5
## - forty1 1 10.41 17373 -12532.2
## - NE 1 14.49 17377 -12525.7
## - height 1 19.40 17382 -12518.0
## - avg_rbry_plyr 1 30.22 17393 -12500.9
## - avg_fuml_plyr 1 239.38 17602 -12172.3
## - avg_qbtdp_plyr 1 2400.61 19763 -8989.4
##
## Step: AIC=-12548.47
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYJ +
## OAK + PHI + PIT + SD + STL + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - STL 1 0.16 17363 -12550.2
## - DEN 1 0.21 17363 -12550.1
## - CIN 1 0.36 17363 -12549.9
## - DET 1 0.37 17363 -12549.9
## - IND 1 0.44 17363 -12549.8
## - NOR 1 0.61 17364 -12549.5
## - DAL 1 0.72 17364 -12549.3
## - home_team_1 1 0.84 17364 -12549.1
## - cold_weather 1 0.98 17364 -12548.9
## - PIT 1 0.99 17364 -12548.9
## - ATL 1 1.01 17364 -12548.9
## - BAL 1 1.03 17364 -12548.8
## - BUF 1 1.26 17364 -12548.5
## <none> 17363 -12548.5
## - vertical1 1 1.43 17364 -12548.2
## - SD 1 1.57 17365 -12548.0
## - HOU 1 1.74 17365 -12547.7
## - bad_weather_1 1 1.85 17365 -12547.5
## - WAS 1 1.88 17365 -12547.5
## - ARI 1 1.97 17365 -12547.3
## - MINN 1 2.26 17365 -12546.9
## - OAK 1 2.31 17365 -12546.8
## - PHI 1 2.32 17365 -12546.8
## - NYJ 1 2.32 17365 -12546.8
## - CAR 1 3.34 17366 -12545.2
## - avg_rbry_pos 1 3.67 17367 -12544.7
## - CLE 1 3.72 17367 -12544.6
## - JAC 1 5.09 17368 -12542.4
## - avg_rectd_plyr 1 7.20 17370 -12539.1
## - GB 1 9.24 17372 -12535.9
## - weight 1 9.63 17373 -12535.2
## - forty1 1 10.41 17373 -12534.0
## - NE 1 14.52 17378 -12527.5
## - height 1 19.42 17382 -12519.8
## - avg_rbry_plyr 1 30.19 17393 -12502.7
## - avg_fuml_plyr 1 239.37 17602 -12174.2
## - avg_qbtdp_plyr 1 2400.57 19764 -8991.3
##
## Step: AIC=-12550.23
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYJ +
## OAK + PHI + PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DEN 1 0.26 17363 -12551.8
## - CIN 1 0.31 17363 -12551.7
## - IND 1 0.38 17364 -12551.6
## - DET 1 0.44 17364 -12551.5
## - NOR 1 0.69 17364 -12551.1
## - DAL 1 0.82 17364 -12550.9
## - BAL 1 0.96 17364 -12550.7
## - cold_weather 1 0.96 17364 -12550.7
## - home_team_1 1 0.96 17364 -12550.7
## - PIT 1 1.09 17364 -12550.5
## - ATL 1 1.14 17364 -12550.4
## - BUF 1 1.18 17364 -12550.4
## <none> 17363 -12550.2
## - vertical1 1 1.46 17365 -12549.9
## - HOU 1 1.63 17365 -12549.6
## - SD 1 1.69 17365 -12549.5
## - WAS 1 1.79 17365 -12549.4
## - bad_weather_1 1 1.82 17365 -12549.3
## - ARI 1 1.86 17365 -12549.3
## - MINN 1 2.15 17365 -12548.8
## - OAK 1 2.20 17365 -12548.7
## - PHI 1 2.22 17365 -12548.7
## - NYJ 1 2.22 17365 -12548.7
## - CAR 1 3.23 17366 -12547.1
## - CLE 1 3.60 17367 -12546.5
## - avg_rbry_pos 1 3.66 17367 -12546.4
## - JAC 1 4.96 17368 -12544.4
## - avg_rectd_plyr 1 7.29 17370 -12540.7
## - GB 1 9.59 17373 -12537.0
## - weight 1 9.70 17373 -12536.9
## - forty1 1 10.46 17374 -12535.7
## - NE 1 15.00 17378 -12528.5
## - height 1 19.46 17383 -12521.4
## - avg_rbry_plyr 1 30.27 17393 -12504.4
## - avg_fuml_plyr 1 239.56 17603 -12175.6
## - avg_qbtdp_plyr 1 2403.30 19766 -8989.3
##
## Step: AIC=-12551.82
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + CLE + DAL +
## DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYJ + OAK +
## PHI + PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CIN 1 0.38 17364 -12553.2
## - DET 1 0.38 17364 -12553.2
## - IND 1 0.46 17364 -12553.1
## - NOR 1 0.61 17364 -12552.8
## - DAL 1 0.74 17364 -12552.7
## - cold_weather 1 0.93 17364 -12552.3
## - PIT 1 0.99 17364 -12552.3
## - home_team_1 1 1.00 17364 -12552.2
## - ATL 1 1.05 17364 -12552.2
## - BAL 1 1.08 17364 -12552.1
## <none> 17363 -12551.8
## - BUF 1 1.31 17365 -12551.8
## - vertical1 1 1.52 17365 -12551.4
## - SD 1 1.58 17365 -12551.3
## - HOU 1 1.77 17365 -12551.0
## - bad_weather_1 1 1.85 17365 -12550.9
## - WAS 1 1.96 17365 -12550.7
## - ARI 1 2.01 17365 -12550.6
## - MINN 1 2.32 17366 -12550.1
## - OAK 1 2.38 17366 -12550.1
## - PHI 1 2.40 17366 -12550.0
## - NYJ 1 2.41 17366 -12550.0
## - CAR 1 3.45 17367 -12548.4
## - avg_rbry_pos 1 3.65 17367 -12548.0
## - CLE 1 3.84 17367 -12547.7
## - JAC 1 5.25 17369 -12545.5
## - avg_rectd_plyr 1 7.45 17371 -12542.0
## - GB 1 9.36 17373 -12539.0
## - weight 1 9.71 17373 -12538.5
## - forty1 1 10.39 17374 -12537.4
## - NE 1 14.75 17378 -12530.5
## - height 1 19.60 17383 -12522.8
## - avg_rbry_plyr 1 30.25 17394 -12506.0
## - avg_fuml_plyr 1 239.46 17603 -12177.4
## - avg_qbtdp_plyr 1 2403.64 19767 -8990.5
##
## Step: AIC=-12553.22
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + DET +
## GB + HOU + IND + JAC + MINN + NE + NOR + NYJ + OAK + PHI +
## PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - IND 1 0.39 17364 -12554.6
## - DET 1 0.45 17364 -12554.5
## - NOR 1 0.71 17364 -12554.1
## - DAL 1 0.84 17365 -12553.9
## - BAL 1 0.97 17365 -12553.7
## - cold_weather 1 0.98 17365 -12553.7
## - home_team_1 1 0.99 17365 -12553.7
## - PIT 1 1.11 17365 -12553.5
## - ATL 1 1.17 17365 -12553.4
## - BUF 1 1.19 17365 -12553.3
## <none> 17364 -12553.2
## - vertical1 1 1.53 17365 -12552.8
## - HOU 1 1.65 17365 -12552.6
## - SD 1 1.73 17366 -12552.5
## - WAS 1 1.83 17366 -12552.3
## - bad_weather_1 1 1.87 17366 -12552.3
## - ARI 1 1.88 17366 -12552.2
## - MINN 1 2.18 17366 -12551.8
## - OAK 1 2.23 17366 -12551.7
## - PHI 1 2.25 17366 -12551.7
## - NYJ 1 2.26 17366 -12551.6
## - CAR 1 3.28 17367 -12550.0
## - avg_rbry_pos 1 3.66 17367 -12549.4
## - CLE 1 3.66 17367 -12549.4
## - JAC 1 5.05 17369 -12547.2
## - avg_rectd_plyr 1 7.46 17371 -12543.4
## - GB 1 9.81 17374 -12539.7
## - weight 1 9.88 17374 -12539.6
## - forty1 1 10.48 17374 -12538.6
## - NE 1 15.35 17379 -12530.9
## - height 1 19.76 17384 -12524.0
## - avg_rbry_plyr 1 30.14 17394 -12507.6
## - avg_fuml_plyr 1 239.26 17603 -12179.1
## - avg_qbtdp_plyr 1 2403.48 19767 -8992.2
##
## Step: AIC=-12554.6
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + DET +
## GB + HOU + JAC + MINN + NE + NOR + NYJ + OAK + PHI + PIT +
## SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DET 1 0.54 17365 -12555.8
## - NOR 1 0.83 17365 -12555.3
## - BAL 1 0.88 17365 -12555.2
## - cold_weather 1 0.95 17365 -12555.1
## - DAL 1 0.97 17365 -12555.1
## - BUF 1 1.09 17365 -12554.9
## - home_team_1 1 1.16 17365 -12554.8
## - PIT 1 1.23 17365 -12554.7
## <none> 17364 -12554.6
## - ATL 1 1.32 17365 -12554.5
## - vertical1 1 1.49 17366 -12554.3
## - HOU 1 1.51 17366 -12554.2
## - WAS 1 1.70 17366 -12553.9
## - ARI 1 1.73 17366 -12553.9
## - bad_weather_1 1 1.86 17366 -12553.7
## - SD 1 1.87 17366 -12553.6
## - MINN 1 2.04 17366 -12553.4
## - OAK 1 2.09 17366 -12553.3
## - PHI 1 2.12 17366 -12553.3
## - NYJ 1 2.12 17366 -12553.2
## - CAR 1 3.12 17367 -12551.7
## - CLE 1 3.50 17368 -12551.1
## - avg_rbry_pos 1 3.61 17368 -12550.9
## - JAC 1 4.85 17369 -12548.9
## - avg_rectd_plyr 1 7.39 17372 -12544.9
## - weight 1 9.74 17374 -12541.2
## - GB 1 10.23 17374 -12540.4
## - forty1 1 10.43 17375 -12540.1
## - NE 1 15.86 17380 -12531.5
## - height 1 19.54 17384 -12525.7
## - avg_rbry_plyr 1 30.13 17394 -12509.0
## - avg_fuml_plyr 1 239.12 17603 -12180.7
## - avg_qbtdp_plyr 1 2411.73 19776 -8982.2
##
## Step: AIC=-12555.75
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + GB +
## HOU + JAC + MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NOR 1 0.71 17365 -12556.6
## - DAL 1 0.85 17366 -12556.4
## - BAL 1 0.99 17366 -12556.2
## - home_team_1 1 1.03 17366 -12556.1
## - cold_weather 1 1.05 17366 -12556.1
## - PIT 1 1.13 17366 -12556.0
## - ATL 1 1.18 17366 -12555.9
## - BUF 1 1.21 17366 -12555.8
## <none> 17365 -12555.8
## - vertical1 1 1.57 17366 -12555.3
## - HOU 1 1.69 17366 -12555.1
## - SD 1 1.73 17366 -12555.0
## - WAS 1 1.85 17367 -12554.8
## - bad_weather_1 1 1.85 17367 -12554.8
## - ARI 1 1.92 17367 -12554.7
## - MINN 1 2.21 17367 -12554.3
## - OAK 1 2.27 17367 -12554.2
## - PHI 1 2.28 17367 -12554.1
## - NYJ 1 2.30 17367 -12554.1
## - CAR 1 3.33 17368 -12552.5
## - avg_rbry_pos 1 3.50 17368 -12552.2
## - CLE 1 3.70 17368 -12551.9
## - JAC 1 5.13 17370 -12549.6
## - avg_rectd_plyr 1 7.62 17372 -12545.7
## - weight 1 9.77 17374 -12542.3
## - GB 1 9.94 17375 -12542.0
## - forty1 1 10.33 17375 -12541.4
## - NE 1 15.52 17380 -12533.2
## - height 1 19.59 17384 -12526.8
## - avg_rbry_plyr 1 29.89 17395 -12510.5
## - avg_fuml_plyr 1 238.84 17604 -12182.3
## - avg_qbtdp_plyr 1 2411.25 19776 -8984.1
##
## Step: AIC=-12556.62
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + GB +
## HOU + JAC + MINN + NE + NYJ + OAK + PHI + PIT + SD + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DAL 1 0.72 17366 -12557.5
## - home_team_1 1 0.92 17366 -12557.2
## - PIT 1 1.01 17366 -12557.0
## - ATL 1 1.02 17366 -12557.0
## - BAL 1 1.12 17367 -12556.8
## - cold_weather 1 1.13 17367 -12556.8
## <none> 17365 -12556.6
## - BUF 1 1.35 17367 -12556.5
## - vertical1 1 1.57 17367 -12556.1
## - SD 1 1.58 17367 -12556.1
## - bad_weather_1 1 1.83 17367 -12555.7
## - HOU 1 1.89 17367 -12555.6
## - WAS 1 2.02 17367 -12555.4
## - ARI 1 2.13 17368 -12555.2
## - MINN 1 2.38 17368 -12554.8
## - PHI 1 2.46 17368 -12554.7
## - OAK 1 2.48 17368 -12554.7
## - NYJ 1 2.48 17368 -12554.7
## - avg_rbry_pos 1 3.33 17369 -12553.4
## - CAR 1 3.57 17369 -12553.0
## - CLE 1 3.91 17369 -12552.4
## - JAC 1 5.44 17371 -12550.0
## - avg_rectd_plyr 1 8.14 17374 -12545.7
## - GB 1 9.56 17375 -12543.5
## - weight 1 9.82 17375 -12543.1
## - forty1 1 10.42 17376 -12542.1
## - NE 1 15.07 17380 -12534.8
## - height 1 19.69 17385 -12527.5
## - avg_rbry_plyr 1 29.73 17395 -12511.6
## - avg_fuml_plyr 1 240.61 17606 -12180.4
## - avg_qbtdp_plyr 1 2420.52 19786 -8972.2
##
## Step: AIC=-12557.49
## ints ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + GB + HOU +
## JAC + MINN + NE + NYJ + OAK + PHI + PIT + SD + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - home_team_1 1 0.74 17367 -12558.3
## - ATL 1 0.89 17367 -12558.1
## - PIT 1 0.91 17367 -12558.0
## - cold_weather 1 1.19 17367 -12557.6
## - BAL 1 1.24 17367 -12557.5
## <none> 17366 -12557.5
## - SD 1 1.45 17368 -12557.2
## - BUF 1 1.47 17368 -12557.2
## - vertical1 1 1.55 17368 -12557.0
## - bad_weather_1 1 1.82 17368 -12556.6
## - HOU 1 2.10 17368 -12556.2
## - WAS 1 2.17 17368 -12556.1
## - ARI 1 2.35 17368 -12555.8
## - MINN 1 2.56 17369 -12555.4
## - PHI 1 2.63 17369 -12555.3
## - NYJ 1 2.65 17369 -12555.3
## - OAK 1 2.67 17369 -12555.3
## - avg_rbry_pos 1 3.32 17369 -12554.2
## - CAR 1 3.78 17370 -12553.5
## - CLE 1 4.10 17370 -12553.0
## - JAC 1 5.70 17372 -12550.5
## - avg_rectd_plyr 1 8.34 17374 -12546.3
## - GB 1 9.26 17375 -12544.8
## - weight 1 9.76 17376 -12544.0
## - forty1 1 10.40 17377 -12543.0
## - NE 1 14.71 17381 -12536.2
## - height 1 19.64 17386 -12528.4
## - avg_rbry_plyr 1 29.91 17396 -12512.2
## - avg_fuml_plyr 1 240.97 17607 -12180.7
## - avg_qbtdp_plyr 1 2419.81 19786 -8974.2
##
## Step: AIC=-12558.32
## ints ~ height + weight + cold_weather + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CLE + GB + HOU + JAC + MINN +
## NE + NYJ + OAK + PHI + PIT + SD + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ATL 1 0.72 17368 -12559.2
## - PIT 1 0.98 17368 -12558.8
## - cold_weather 1 1.03 17368 -12558.7
## - BAL 1 1.17 17368 -12558.5
## <none> 17367 -12558.3
## - BUF 1 1.42 17368 -12558.1
## - vertical1 1 1.55 17368 -12557.9
## - SD 1 1.55 17368 -12557.9
## - bad_weather_1 1 1.75 17369 -12557.6
## - WAS 1 2.05 17369 -12557.1
## - HOU 1 2.43 17369 -12556.5
## - PHI 1 2.53 17369 -12556.3
## - MINN 1 2.54 17369 -12556.3
## - OAK 1 2.56 17369 -12556.3
## - NYJ 1 2.56 17369 -12556.3
## - ARI 1 2.70 17370 -12556.0
## - avg_rbry_pos 1 3.34 17370 -12555.0
## - CAR 1 3.63 17371 -12554.6
## - CLE 1 3.96 17371 -12554.0
## - JAC 1 5.52 17372 -12551.6
## - avg_rectd_plyr 1 8.27 17375 -12547.2
## - GB 1 9.47 17376 -12545.3
## - weight 1 9.76 17377 -12544.9
## - forty1 1 10.43 17377 -12543.8
## - NE 1 15.05 17382 -12536.5
## - height 1 19.60 17386 -12529.3
## - avg_rbry_plyr 1 29.92 17397 -12513.0
## - avg_fuml_plyr 1 240.75 17608 -12181.9
## - avg_qbtdp_plyr 1 2421.14 19788 -8973.3
##
## Step: AIC=-12559.17
## ints ~ height + weight + cold_weather + forty1 + vertical1 +
## ARI + BAL + BUF + CAR + CLE + GB + HOU + JAC + MINN + NE +
## NYJ + OAK + PHI + PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PIT 1 0.89 17368 -12559.8
## - cold_weather 1 1.17 17369 -12559.3
## <none> 17368 -12559.2
## - BAL 1 1.28 17369 -12559.1
## - SD 1 1.42 17369 -12558.9
## - vertical1 1 1.45 17369 -12558.9
## - BUF 1 1.54 17369 -12558.7
## - bad_weather_1 1 1.77 17369 -12558.4
## - WAS 1 2.20 17370 -12557.7
## - HOU 1 2.62 17370 -12557.0
## - MINN 1 2.68 17370 -12556.9
## - PHI 1 2.70 17370 -12556.9
## - NYJ 1 2.71 17370 -12556.9
## - OAK 1 2.74 17370 -12556.8
## - ARI 1 2.88 17370 -12556.6
## - avg_rbry_pos 1 3.30 17371 -12556.0
## - CAR 1 3.84 17371 -12555.1
## - CLE 1 4.14 17372 -12554.6
## - JAC 1 5.79 17373 -12552.0
## - avg_rectd_plyr 1 8.55 17376 -12547.6
## - GB 1 9.17 17377 -12546.7
## - weight 1 9.79 17377 -12545.7
## - forty1 1 10.39 17378 -12544.7
## - NE 1 14.65 17382 -12538.0
## - height 1 19.88 17387 -12529.7
## - avg_rbry_plyr 1 29.95 17398 -12513.8
## - avg_fuml_plyr 1 242.63 17610 -12179.9
## - avg_qbtdp_plyr 1 2421.52 19789 -8973.8
##
## Step: AIC=-12559.76
## ints ~ height + weight + cold_weather + forty1 + vertical1 +
## ARI + BAL + BUF + CAR + CLE + GB + HOU + JAC + MINN + NE +
## NYJ + OAK + PHI + SD + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - cold_weather 1 0.99 17369 -12560.2
## <none> 17368 -12559.8
## - SD 1 1.31 17370 -12559.7
## - BAL 1 1.43 17370 -12559.5
## - vertical1 1 1.44 17370 -12559.5
## - BUF 1 1.70 17370 -12559.1
## - bad_weather_1 1 1.73 17370 -12559.0
## - WAS 1 2.39 17371 -12558.0
## - HOU 1 2.79 17371 -12557.3
## - MINN 1 2.88 17371 -12557.2
## - PHI 1 2.90 17371 -12557.2
## - NYJ 1 2.93 17371 -12557.1
## - OAK 1 2.93 17371 -12557.1
## - ARI 1 3.08 17372 -12556.9
## - avg_rbry_pos 1 3.29 17372 -12556.6
## - CAR 1 4.08 17373 -12555.3
## - CLE 1 4.42 17373 -12554.8
## - JAC 1 6.04 17375 -12552.2
## - avg_rectd_plyr 1 8.64 17377 -12548.1
## - GB 1 8.81 17377 -12547.8
## - weight 1 9.79 17378 -12546.3
## - forty1 1 10.41 17379 -12545.3
## - NE 1 14.23 17383 -12539.3
## - height 1 19.87 17388 -12530.3
## - avg_rbry_plyr 1 29.96 17398 -12514.4
## - avg_fuml_plyr 1 242.17 17611 -12181.2
## - avg_qbtdp_plyr 1 2422.08 19791 -8973.8
##
## Step: AIC=-12560.2
## ints ~ height + weight + forty1 + vertical1 + ARI + BAL + BUF +
## CAR + CLE + GB + HOU + JAC + MINN + NE + NYJ + OAK + PHI +
## SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
##
## Df Sum of Sq RSS AIC
## <none> 17369 -12560.2
## - SD 1 1.37 17371 -12560.0
## - vertical1 1 1.42 17371 -12559.9
## - BAL 1 1.57 17371 -12559.7
## - BUF 1 1.79 17371 -12559.4
## - bad_weather_1 1 2.16 17372 -12558.8
## - WAS 1 2.43 17372 -12558.4
## - HOU 1 2.62 17372 -12558.1
## - OAK 1 2.81 17372 -12557.7
## - MINN 1 2.92 17372 -12557.6
## - PHI 1 2.99 17372 -12557.5
## - ARI 1 2.99 17372 -12557.5
## - NYJ 1 3.03 17373 -12557.4
## - avg_rbry_pos 1 3.26 17373 -12557.0
## - CAR 1 4.05 17374 -12555.8
## - CLE 1 4.71 17374 -12554.7
## - JAC 1 5.84 17375 -12553.0
## - GB 1 8.39 17378 -12548.9
## - avg_rectd_plyr 1 8.75 17378 -12548.4
## - weight 1 9.74 17379 -12546.8
## - forty1 1 10.42 17380 -12545.7
## - NE 1 13.78 17383 -12540.4
## - height 1 19.82 17389 -12530.8
## - avg_rbry_plyr 1 29.92 17399 -12514.9
## - avg_fuml_plyr 1 242.03 17612 -12181.9
## - avg_qbtdp_plyr 1 2422.00 19791 -8974.5Pass Attempts
PreProcess:
set.seed(123)
splitpa <- sample.split(nfl_data$pa, SplitRatio = 0.7)
Trainpa <- subset(nfl_data, split == TRUE)
Testpa <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainpa, method = c("center", "scale"))
trainTransformedpa <- predict(preProcValues, Trainpa)
testTransformedpa <- predict(preProcValues, Testpa)ggpairs:
ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[46:51]))])
paregform <- formula(paste("pa ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegQBpa <- lm(paregform, data = trainTransformedpa)
summary(linRegQBpa)##
## Call:
## lm(formula = paregform, data = trainTransformedpa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1030 -0.0669 -0.0157 0.0397 4.5224
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.763e-15 2.304e-03 0.000 1.000000
## height 5.881e-02 4.470e-03 13.158 < 2e-16 ***
## weight -3.669e-02 4.189e-03 -8.758 < 2e-16 ***
## cold_weather -1.546e-03 2.425e-03 -0.638 0.523669
## hot_weather -1.288e-03 2.325e-03 -0.554 0.579429
## home_team_1 -3.172e-03 2.506e-03 -1.265 0.205762
## forty1 2.154e-02 3.976e-03 5.418 6.07e-08 ***
## vertical1 -1.677e-02 3.057e-03 -5.486 4.15e-08 ***
## ARI 7.868e-04 3.222e-03 0.244 0.807111
## ATL -8.184e-03 3.238e-03 -2.528 0.011491 *
## BAL -1.113e-04 3.241e-03 -0.034 0.972591
## BUF 8.983e-04 3.199e-03 0.281 0.778850
## CAR -1.715e-03 3.178e-03 -0.540 0.589378
## CHI -8.235e-03 3.143e-03 -2.620 0.008787 **
## CIN -5.600e-03 3.201e-03 -1.750 0.080182 .
## CLE 8.330e-03 3.186e-03 2.615 0.008932 **
## DAL -1.518e-02 3.218e-03 -4.716 2.41e-06 ***
## DEN -6.895e-03 3.230e-03 -2.134 0.032813 *
## DET -4.745e-03 3.186e-03 -1.489 0.136370
## GB -2.153e-02 3.280e-03 -6.563 5.37e-11 ***
## HOU 7.181e-03 3.241e-03 2.216 0.026717 *
## IND -4.968e-03 3.217e-03 -1.544 0.122511
## JAC 3.626e-03 3.138e-03 1.156 0.247868
## KC 3.694e-03 3.207e-03 1.152 0.249377
## MIA -1.993e-03 3.155e-03 -0.632 0.527592
## MINN 4.361e-03 3.175e-03 1.374 0.169503
## NE -1.871e-02 3.316e-03 -5.644 1.68e-08 ***
## NOR -1.518e-02 3.305e-03 -4.593 4.38e-06 ***
## NYG -1.148e-02 3.231e-03 -3.554 0.000381 ***
## NYJ -2.603e-03 3.219e-03 -0.809 0.418613
## OAK -2.043e-03 3.239e-03 -0.631 0.528265
## PHI 3.831e-03 3.139e-03 1.221 0.222250
## PIT -7.229e-03 3.221e-03 -2.244 0.024827 *
## SD -1.680e-02 3.161e-03 -5.315 1.08e-07 ***
## SEA -2.060e-03 3.281e-03 -0.628 0.530075
## STL 3.392e-03 3.193e-03 1.062 0.288105
## TB -6.161e-03 3.163e-03 -1.948 0.051430 .
## TEN -5.033e-03 3.182e-03 -1.582 0.113715
## WAS 2.904e-03 3.199e-03 0.908 0.364056
## avg_trg_team NA NA NA NA
## avg_rectd_plyr -2.016e-02 2.942e-03 -6.854 7.34e-12 ***
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr -3.353e-02 3.520e-03 -9.525 < 2e-16 ***
## avg_rbry_pos 1.909e-02 4.102e-03 4.654 3.26e-06 ***
## avg_fuml_plyr 1.015e-01 3.403e-03 29.822 < 2e-16 ***
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr 8.223e-01 3.696e-03 222.466 < 2e-16 ***
## avg_qbtdp_team NA NA NA NA
## grass_1 -7.378e-04 2.650e-03 -0.278 0.780742
## bad_weather_1 -4.319e-04 2.343e-03 -0.184 0.853791
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3819 on 27438 degrees of freedom
## Multiple R-squared: 0.8544, Adjusted R-squared: 0.8541
## F-statistic: 3578 on 45 and 27438 DF, p-value: < 2.2e-16linRegQBpa2 <- update(linRegQBpa, ~.-hot_weather-home_team_1-ATL-BAL-CLE-DAL-DEN-DET-KC
-NOR-OAK-SEA-STL-WAS-avg_trg_team-avg_tdr_team-avg_rbra_team
-avg_rbry_plyr-avg_fuml_team-avg_qbints_team-avg_qbtdp_team
-grass_1-bad_weather_1 )
summary(linRegQBpa2)##
## Call:
## lm(formula = pa ~ height + weight + cold_weather + forty1 + vertical1 +
## ARI + BUF + CAR + CHI + CIN + GB + HOU + IND + JAC + MIA +
## MINN + NE + NYG + NYJ + PHI + PIT + SD + TB + TEN + avg_rectd_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr, data = trainTransformedpa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1273 -0.0684 -0.0140 0.0358 4.5162
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.823e-15 2.311e-03 0.000 1.00000
## height 5.863e-02 4.448e-03 13.180 < 2e-16 ***
## weight -3.843e-02 4.181e-03 -9.192 < 2e-16 ***
## cold_weather 5.948e-04 2.362e-03 0.252 0.80116
## forty1 2.767e-02 3.912e-03 7.074 1.54e-12 ***
## vertical1 -1.494e-02 3.046e-03 -4.907 9.30e-07 ***
## ARI 4.500e-03 2.365e-03 1.903 0.05706 .
## BUF 3.347e-03 2.367e-03 1.414 0.15738
## CAR 1.515e-04 2.363e-03 0.064 0.94888
## CHI -6.221e-03 2.367e-03 -2.628 0.00858 **
## CIN -3.585e-03 2.366e-03 -1.516 0.12965
## GB -1.914e-02 2.388e-03 -8.012 1.17e-15 ***
## HOU 9.804e-03 2.372e-03 4.133 3.59e-05 ***
## IND -1.935e-03 2.363e-03 -0.819 0.41288
## JAC 5.974e-03 2.365e-03 2.526 0.01153 *
## MIA 9.219e-04 2.360e-03 0.391 0.69600
## MINN 5.977e-03 2.369e-03 2.523 0.01163 *
## NE -1.654e-02 2.416e-03 -6.849 7.60e-12 ***
## NYG -8.542e-03 2.368e-03 -3.608 0.00031 ***
## NYJ -6.759e-04 2.369e-03 -0.285 0.77535
## PHI 5.807e-03 2.363e-03 2.458 0.01399 *
## PIT -4.942e-03 2.373e-03 -2.082 0.03731 *
## SD -1.396e-02 2.365e-03 -5.904 3.60e-09 ***
## TB -3.594e-03 2.363e-03 -1.521 0.12829
## TEN -2.594e-03 2.364e-03 -1.097 0.27262
## avg_rectd_plyr -2.529e-02 2.907e-03 -8.700 < 2e-16 ***
## avg_rbry_pos -4.926e-03 3.434e-03 -1.434 0.15146
## avg_fuml_plyr 9.268e-02 3.205e-03 28.919 < 2e-16 ***
## avg_qbtdp_plyr 8.233e-01 3.645e-03 225.904 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3832 on 27455 degrees of freedom
## Multiple R-squared: 0.8533, Adjusted R-squared: 0.8532
## F-statistic: 5704 on 28 and 27455 DF, p-value: < 2.2e-16linRegQBpa3 <- update(linRegQBpa2, ~.-vertical1-IND-PHI-PIT )
summary(linRegQBpa3)##
## Call:
## lm(formula = pa ~ height + weight + cold_weather + forty1 + ARI +
## BUF + CAR + CHI + CIN + GB + HOU + JAC + MIA + MINN + NE +
## NYG + NYJ + SD + TB + TEN + avg_rectd_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr, data = trainTransformedpa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1362 -0.0694 -0.0130 0.0356 4.5346
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.837e-15 2.313e-03 0.000 1.000000
## height 5.816e-02 4.447e-03 13.079 < 2e-16 ***
## weight -3.996e-02 4.171e-03 -9.580 < 2e-16 ***
## cold_weather 1.311e-04 2.351e-03 0.056 0.955524
## forty1 3.773e-02 3.342e-03 11.290 < 2e-16 ***
## ARI 4.865e-03 2.351e-03 2.069 0.038516 *
## BUF 3.949e-03 2.351e-03 1.680 0.093004 .
## CAR 1.089e-04 2.349e-03 0.046 0.963033
## CHI -5.742e-03 2.352e-03 -2.441 0.014637 *
## CIN -3.356e-03 2.351e-03 -1.427 0.153498
## GB -1.861e-02 2.370e-03 -7.849 4.34e-15 ***
## HOU 9.521e-03 2.359e-03 4.037 5.44e-05 ***
## JAC 5.286e-03 2.348e-03 2.251 0.024380 *
## MIA 1.332e-03 2.346e-03 0.568 0.570156
## MINN 5.619e-03 2.355e-03 2.386 0.017022 *
## NE -1.624e-02 2.400e-03 -6.768 1.33e-11 ***
## NYG -8.348e-03 2.353e-03 -3.548 0.000389 ***
## NYJ -1.280e-03 2.350e-03 -0.544 0.586103
## SD -1.374e-02 2.353e-03 -5.841 5.25e-09 ***
## TB -3.308e-03 2.350e-03 -1.408 0.159203
## TEN -2.767e-03 2.350e-03 -1.177 0.239039
## avg_rectd_plyr -2.617e-02 2.904e-03 -9.010 < 2e-16 ***
## avg_rbry_pos -4.051e-03 3.427e-03 -1.182 0.237211
## avg_fuml_plyr 9.350e-02 3.199e-03 29.232 < 2e-16 ***
## avg_qbtdp_plyr 8.231e-01 3.643e-03 225.966 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3834 on 27459 degrees of freedom
## Multiple R-squared: 0.8531, Adjusted R-squared: 0.853
## F-statistic: 6645 on 24 and 27459 DF, p-value: < 2.2e-16R2 is strong. This stat is the catalyst Ints, completions, TD’s. You have to attempt a pass in order to achieve a stat in any of these three categories.
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
PaPredicted <- predict(linRegQBpa3, newdata = testTransformedpa)
SSEpa <- sum((PaPredicted - testTransformedpa$pa)^2)
SSTpa <- sum((mean(nfl_data$pa)-testTransformedpa$pa)^2)
r2_pa <- 1 - SSEpa/SSTpa
r2_pa## [1] 0.9870137rmse_pa <- sqrt(SSEpa/nrow(testTransformedpa))
rmse_pa## [1] 0.3953472Regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBpa3, which = c(1:3,5))
Very similar patterns to completions and yards. Some strong tails, so the data may not be normally distributed
Summary statistics:
confint(linRegQBpa3)## 2.5 % 97.5 %
## (Intercept) -0.0045332724 0.004533272
## height 0.0494453252 0.066877140
## weight -0.0481324757 -0.031781419
## cold_weather -0.0044762676 0.004738466
## forty1 0.0311803541 0.044281015
## ARI 0.0002571222 0.009472993
## BUF -0.0006588596 0.008557851
## CAR -0.0044955296 0.004713284
## CHI -0.0103515944 -0.001132075
## CIN -0.0079650992 0.001252658
## GB -0.0232514031 -0.013959285
## HOU 0.0048978676 0.014143962
## JAC 0.0006836263 0.009887708
## MIA -0.0032657529 0.005929682
## MINN 0.0010038754 0.010234782
## NE -0.0209465699 -0.011538645
## NYG -0.0129596970 -0.003735903
## NYJ -0.0058856085 0.003326504
## SD -0.0183540586 -0.009130940
## TB -0.0079143787 0.001297788
## TEN -0.0073740699 0.001839441
## avg_rectd_plyr -0.0318627125 -0.020476836
## avg_rbry_pos -0.0107684004 0.002666476
## avg_fuml_plyr 0.0872311724 0.099770017
## avg_qbtdp_plyr 0.8159438330 0.830222848coef(summary(linRegQBpa3))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.837106e-15 0.002312835 1.226679e-12 1.000000e+00
## height 5.816123e-02 0.004446777 1.307941e+01 5.647188e-39
## weight -3.995695e-02 0.004171081 -9.579519e+00 1.054241e-21
## cold_weather 1.310994e-04 0.002350637 5.577188e-02 9.555239e-01
## forty1 3.773068e-02 0.003341919 1.129012e+01 1.705538e-29
## ARI 4.865058e-03 0.002350927 2.069421e+00 3.851593e-02
## BUF 3.949496e-03 0.002351141 1.679821e+00 9.300359e-02
## CAR 1.088773e-04 0.002349127 4.634798e-02 9.630332e-01
## CHI -5.741835e-03 0.002351858 -2.441404e+00 1.463656e-02
## CIN -3.356220e-03 0.002351408 -1.427324e+00 1.534980e-01
## GB -1.860534e-02 0.002370377 -7.849106e+00 4.342062e-15
## HOU 9.520915e-03 0.002358637 4.036617e+00 5.437438e-05
## JAC 5.285667e-03 0.002347920 2.251213e+00 2.437993e-02
## MIA 1.331964e-03 0.002345714 5.678290e-01 5.701557e-01
## MINN 5.619329e-03 0.002354763 2.386367e+00 1.702247e-02
## NE -1.624261e-02 0.002399919 -6.767981e+00 1.332176e-11
## NYG -8.347800e-03 0.002352948 -3.547804e+00 3.891041e-04
## NYJ -1.279552e-03 0.002349968 -5.444977e-01 5.861035e-01
## SD -1.374250e-02 0.002352776 -5.840972e+00 5.248161e-09
## TB -3.308296e-03 0.002349982 -1.407796e+00 1.592028e-01
## TEN -2.767315e-03 0.002350325 -1.177418e+00 2.390390e-01
## avg_rectd_plyr -2.616977e-02 0.002904486 -9.010123e+00 2.188484e-19
## avg_rbry_pos -4.050962e-03 0.003427176 -1.182012e+00 2.372113e-01
## avg_fuml_plyr 9.350059e-02 0.003198603 2.923170e+01 5.249398e-185
## avg_qbtdp_plyr 8.230833e-01 0.003642512 2.259658e+02 0.000000e+00anova(linRegQBpa3)## Analysis of Variance Table
##
## Response: pa
## Df Sum Sq Mean Sq F value Pr(>F)
## height 1 1950.3 1950.3 13265.6253 < 2.2e-16 ***
## weight 1 461.7 461.7 3140.2425 < 2.2e-16 ***
## cold_weather 1 0.0 0.0 0.0000 0.995281
## forty1 1 5580.4 5580.4 37957.4316 < 2.2e-16 ***
## ARI 1 1.3 1.3 8.6924 0.003198 **
## BUF 1 1.2 1.2 8.3499 0.003860 **
## CAR 1 9.9 9.9 67.1807 2.584e-16 ***
## CHI 1 0.3 0.3 2.2304 0.135331
## CIN 1 3.0 3.0 20.5662 5.785e-06 ***
## GB 1 0.2 0.2 1.2281 0.267782
## HOU 1 12.2 12.2 83.0773 < 2.2e-16 ***
## JAC 1 0.8 0.8 5.1288 0.023540 *
## MIA 1 0.4 0.4 2.5248 0.112079
## MINN 1 0.8 0.8 5.7576 0.016424 *
## NE 1 43.7 43.7 297.5004 < 2.2e-16 ***
## NYG 1 8.5 8.5 57.8649 2.897e-14 ***
## NYJ 1 0.2 0.2 1.6841 0.194393
## SD 1 19.9 19.9 135.1058 < 2.2e-16 ***
## TB 1 2.5 2.5 17.3398 3.135e-05 ***
## TEN 1 5.8 5.8 39.2418 3.800e-10 ***
## avg_rectd_plyr 1 1877.2 1877.2 12768.2759 < 2.2e-16 ***
## avg_rbry_pos 1 341.1 341.1 2320.1948 < 2.2e-16 ***
## avg_fuml_plyr 1 5617.8 5617.8 38212.0971 < 2.2e-16 ***
## avg_qbtdp_plyr 1 7506.8 7506.8 51060.5597 < 2.2e-16 ***
## Residuals 27459 4037.0 0.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_pa <- step(lm(paregform, data = trainTransformedpa), direction = "backward")## Start: AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BAL 1 0.0 4001.9 -52867
## - bad_weather_1 1 0.0 4001.9 -52867
## - ARI 1 0.0 4001.9 -52867
## - grass_1 1 0.0 4001.9 -52867
## - BUF 1 0.0 4001.9 -52867
## - CAR 1 0.0 4001.9 -52867
## - hot_weather 1 0.0 4001.9 -52867
## - SEA 1 0.1 4001.9 -52867
## - OAK 1 0.1 4001.9 -52867
## - MIA 1 0.1 4001.9 -52867
## - cold_weather 1 0.1 4001.9 -52867
## - NYJ 1 0.1 4002.0 -52867
## - WAS 1 0.1 4002.0 -52866
## - STL 1 0.2 4002.1 -52866
## - KC 1 0.2 4002.1 -52866
## - JAC 1 0.2 4002.1 -52866
## - PHI 1 0.2 4002.1 -52866
## - home_team_1 1 0.2 4002.1 -52866
## - MINN 1 0.3 4002.2 -52865
## <none> 4001.9 -52865
## - DET 1 0.3 4002.2 -52865
## - IND 1 0.3 4002.2 -52865
## - TEN 1 0.4 4002.3 -52865
## - CIN 1 0.4 4002.3 -52864
## - TB 1 0.6 4002.4 -52863
## - DEN 1 0.7 4002.6 -52863
## - HOU 1 0.7 4002.6 -52862
## - PIT 1 0.7 4002.6 -52862
## - ATL 1 0.9 4002.8 -52861
## - CLE 1 1.0 4002.9 -52860
## - CHI 1 1.0 4002.9 -52860
## - NYG 1 1.8 4003.7 -52855
## - NOR 1 3.1 4005.0 -52846
## - avg_rbry_pos 1 3.2 4005.0 -52846
## - DAL 1 3.2 4005.1 -52845
## - SD 1 4.1 4006.0 -52839
## - forty1 1 4.3 4006.2 -52838
## - vertical1 1 4.4 4006.3 -52837
## - NE 1 4.6 4006.5 -52835
## - GB 1 6.3 4008.2 -52824
## - avg_rectd_plyr 1 6.9 4008.7 -52820
## - weight 1 11.2 4013.1 -52790
## - avg_rbry_plyr 1 13.2 4015.1 -52776
## - height 1 25.3 4027.1 -52694
## - avg_fuml_plyr 1 129.7 4131.6 -51991
## - avg_qbtdp_plyr 1 7218.4 11220.2 -24532
##
## Step: AIC=-52867.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - bad_weather_1 1 0.0 4001.9 -52869
## - grass_1 1 0.0 4001.9 -52869
## - ARI 1 0.0 4001.9 -52869
## - BUF 1 0.0 4001.9 -52869
## - hot_weather 1 0.0 4001.9 -52869
## - CAR 1 0.1 4001.9 -52869
## - cold_weather 1 0.1 4001.9 -52869
## - MIA 1 0.1 4002.0 -52869
## - OAK 1 0.1 4002.0 -52869
## - SEA 1 0.1 4002.0 -52869
## - NYJ 1 0.1 4002.0 -52868
## - WAS 1 0.2 4002.1 -52868
## - STL 1 0.2 4002.1 -52868
## - home_team_1 1 0.2 4002.1 -52868
## - JAC 1 0.3 4002.1 -52867
## - KC 1 0.3 4002.2 -52867
## <none> 4001.9 -52867
## - PHI 1 0.3 4002.2 -52867
## - MINN 1 0.4 4002.3 -52867
## - DET 1 0.4 4002.3 -52866
## - IND 1 0.5 4002.3 -52866
## - TEN 1 0.5 4002.4 -52866
## - CIN 1 0.6 4002.5 -52865
## - TB 1 0.7 4002.6 -52864
## - DEN 1 0.9 4002.8 -52863
## - PIT 1 1.0 4002.9 -52863
## - HOU 1 1.0 4002.9 -52863
## - ATL 1 1.2 4003.1 -52861
## - CHI 1 1.3 4003.2 -52860
## - CLE 1 1.3 4003.2 -52860
## - NYG 1 2.5 4004.3 -52852
## - avg_rbry_pos 1 3.2 4005.0 -52848
## - NOR 1 4.1 4006.0 -52841
## - DAL 1 4.3 4006.2 -52840
## - forty1 1 4.3 4006.2 -52840
## - vertical1 1 4.4 4006.3 -52839
## - SD 1 5.4 4007.2 -52832
## - NE 1 6.2 4008.1 -52826
## - avg_rectd_plyr 1 6.9 4008.7 -52822
## - GB 1 8.4 4010.3 -52811
## - weight 1 11.2 4013.1 -52792
## - avg_rbry_plyr 1 13.2 4015.1 -52778
## - height 1 25.3 4027.1 -52696
## - avg_fuml_plyr 1 129.7 4131.6 -51992
## - avg_qbtdp_plyr 1 7218.4 11220.3 -24534
##
## Step: AIC=-52869.19
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 0.0 4001.9 -52871
## - ARI 1 0.0 4001.9 -52871
## - BUF 1 0.0 4001.9 -52871
## - hot_weather 1 0.0 4001.9 -52871
## - CAR 1 0.1 4001.9 -52871
## - cold_weather 1 0.1 4002.0 -52871
## - MIA 1 0.1 4002.0 -52871
## - OAK 1 0.1 4002.0 -52871
## - SEA 1 0.1 4002.0 -52871
## - NYJ 1 0.1 4002.0 -52870
## - WAS 1 0.2 4002.1 -52870
## - STL 1 0.2 4002.1 -52870
## - home_team_1 1 0.2 4002.1 -52870
## - JAC 1 0.3 4002.2 -52869
## - KC 1 0.3 4002.2 -52869
## <none> 4001.9 -52869
## - PHI 1 0.3 4002.2 -52869
## - MINN 1 0.4 4002.3 -52869
## - DET 1 0.4 4002.3 -52868
## - IND 1 0.5 4002.3 -52868
## - TEN 1 0.5 4002.4 -52868
## - CIN 1 0.6 4002.5 -52867
## - TB 1 0.7 4002.6 -52866
## - DEN 1 0.9 4002.8 -52865
## - HOU 1 1.0 4002.9 -52865
## - PIT 1 1.0 4002.9 -52865
## - ATL 1 1.2 4003.1 -52863
## - CHI 1 1.3 4003.2 -52862
## - CLE 1 1.3 4003.2 -52862
## - NYG 1 2.5 4004.4 -52854
## - avg_rbry_pos 1 3.2 4005.0 -52850
## - NOR 1 4.1 4006.0 -52843
## - DAL 1 4.3 4006.2 -52842
## - forty1 1 4.3 4006.2 -52842
## - vertical1 1 4.4 4006.3 -52841
## - SD 1 5.4 4007.2 -52834
## - NE 1 6.2 4008.1 -52828
## - avg_rectd_plyr 1 6.8 4008.7 -52824
## - GB 1 8.4 4010.3 -52813
## - weight 1 11.2 4013.1 -52794
## - avg_rbry_plyr 1 13.2 4015.1 -52780
## - height 1 25.3 4027.1 -52698
## - avg_fuml_plyr 1 129.7 4131.6 -51994
## - avg_qbtdp_plyr 1 7218.4 11220.3 -24536
##
## Step: AIC=-52871.11
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - ARI 1 0.0 4001.9 -52873
## - BUF 1 0.0 4001.9 -52873
## - hot_weather 1 0.0 4002.0 -52873
## - CAR 1 0.1 4002.0 -52873
## - cold_weather 1 0.1 4002.0 -52873
## - SEA 1 0.1 4002.0 -52873
## - MIA 1 0.1 4002.0 -52873
## - OAK 1 0.1 4002.0 -52873
## - NYJ 1 0.1 4002.0 -52872
## - WAS 1 0.2 4002.1 -52872
## - STL 1 0.2 4002.1 -52872
## - KC 1 0.3 4002.2 -52871
## - home_team_1 1 0.3 4002.2 -52871
## - JAC 1 0.3 4002.2 -52871
## - PHI 1 0.3 4002.2 -52871
## <none> 4001.9 -52871
## - MINN 1 0.4 4002.3 -52870
## - DET 1 0.4 4002.3 -52870
## - IND 1 0.4 4002.3 -52870
## - TEN 1 0.5 4002.4 -52870
## - CIN 1 0.6 4002.5 -52869
## - TB 1 0.7 4002.6 -52868
## - DEN 1 0.9 4002.8 -52867
## - HOU 1 1.0 4002.9 -52866
## - PIT 1 1.0 4002.9 -52866
## - ATL 1 1.2 4003.1 -52865
## - CLE 1 1.3 4003.2 -52864
## - CHI 1 1.3 4003.2 -52864
## - NYG 1 2.5 4004.4 -52856
## - avg_rbry_pos 1 3.2 4005.1 -52851
## - NOR 1 4.1 4006.0 -52845
## - DAL 1 4.3 4006.2 -52844
## - forty1 1 4.3 4006.2 -52844
## - vertical1 1 4.4 4006.3 -52843
## - SD 1 5.4 4007.3 -52836
## - NE 1 6.3 4008.2 -52830
## - avg_rectd_plyr 1 6.9 4008.8 -52826
## - GB 1 8.5 4010.4 -52815
## - weight 1 11.2 4013.1 -52796
## - avg_rbry_plyr 1 13.2 4015.1 -52782
## - height 1 25.3 4027.2 -52700
## - avg_fuml_plyr 1 129.7 4131.6 -51996
## - avg_qbtdp_plyr 1 7218.8 11220.7 -24537
##
## Step: AIC=-52873.01
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.0 4001.9 -52875
## - hot_weather 1 0.0 4002.0 -52875
## - cold_weather 1 0.1 4002.0 -52875
## - CAR 1 0.1 4002.0 -52874
## - SEA 1 0.1 4002.0 -52874
## - MIA 1 0.1 4002.0 -52874
## - OAK 1 0.1 4002.0 -52874
## - WAS 1 0.1 4002.1 -52874
## - NYJ 1 0.2 4002.1 -52874
## - STL 1 0.2 4002.1 -52874
## - KC 1 0.2 4002.2 -52873
## - JAC 1 0.2 4002.2 -52873
## - PHI 1 0.3 4002.2 -52873
## - home_team_1 1 0.3 4002.2 -52873
## <none> 4001.9 -52873
## - MINN 1 0.4 4002.3 -52872
## - DET 1 0.5 4002.4 -52871
## - IND 1 0.6 4002.5 -52871
## - TEN 1 0.6 4002.5 -52871
## - CIN 1 0.7 4002.6 -52870
## - TB 1 0.9 4002.8 -52869
## - HOU 1 1.0 4002.9 -52868
## - DEN 1 1.1 4003.0 -52868
## - PIT 1 1.2 4003.1 -52867
## - CLE 1 1.4 4003.3 -52866
## - ATL 1 1.5 4003.4 -52865
## - CHI 1 1.6 4003.5 -52864
## - NYG 1 2.9 4004.8 -52855
## - avg_rbry_pos 1 3.2 4005.1 -52853
## - forty1 1 4.3 4006.2 -52846
## - vertical1 1 4.4 4006.3 -52845
## - NOR 1 4.9 4006.8 -52842
## - DAL 1 5.0 4006.9 -52841
## - SD 1 6.2 4008.2 -52832
## - avg_rectd_plyr 1 6.9 4008.8 -52828
## - NE 1 7.1 4009.1 -52826
## - GB 1 9.8 4011.7 -52808
## - weight 1 11.2 4013.1 -52798
## - avg_rbry_plyr 1 13.3 4015.2 -52784
## - height 1 25.4 4027.3 -52701
## - avg_fuml_plyr 1 129.9 4131.8 -51997
## - avg_qbtdp_plyr 1 7223.1 11225.0 -24529
##
## Step: AIC=-52874.93
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + CAR + CHI + CIN + CLE + DAL +
## DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.0 4002.0 -52877
## - cold_weather 1 0.1 4002.0 -52876
## - CAR 1 0.1 4002.0 -52876
## - SEA 1 0.1 4002.1 -52876
## - WAS 1 0.1 4002.1 -52876
## - MIA 1 0.1 4002.1 -52876
## - OAK 1 0.1 4002.1 -52876
## - NYJ 1 0.2 4002.1 -52876
## - STL 1 0.2 4002.1 -52875
## - KC 1 0.2 4002.2 -52875
## - JAC 1 0.2 4002.2 -52875
## - PHI 1 0.3 4002.2 -52875
## - home_team_1 1 0.3 4002.2 -52875
## <none> 4001.9 -52875
## - MINN 1 0.4 4002.3 -52874
## - DET 1 0.6 4002.5 -52873
## - IND 1 0.6 4002.6 -52873
## - TEN 1 0.7 4002.6 -52872
## - CIN 1 0.8 4002.7 -52871
## - TB 1 1.0 4002.9 -52870
## - HOU 1 1.0 4003.0 -52870
## - DEN 1 1.2 4003.1 -52869
## - PIT 1 1.3 4003.3 -52868
## - CLE 1 1.4 4003.3 -52867
## - ATL 1 1.6 4003.5 -52866
## - CHI 1 1.7 4003.7 -52865
## - NYG 1 3.2 4005.1 -52855
## - avg_rbry_pos 1 3.2 4005.1 -52855
## - forty1 1 4.3 4006.2 -52848
## - vertical1 1 4.4 4006.4 -52847
## - NOR 1 5.3 4007.2 -52841
## - DAL 1 5.4 4007.3 -52840
## - SD 1 6.8 4008.7 -52831
## - avg_rectd_plyr 1 6.9 4008.8 -52830
## - NE 1 7.7 4009.7 -52824
## - GB 1 10.6 4012.5 -52804
## - weight 1 11.3 4013.2 -52800
## - avg_rbry_plyr 1 13.3 4015.2 -52786
## - height 1 25.4 4027.4 -52703
## - avg_fuml_plyr 1 130.0 4131.9 -51998
## - avg_qbtdp_plyr 1 7226.4 11228.4 -24523
##
## Step: AIC=-52876.61
## pa ~ height + weight + cold_weather + home_team_1 + forty1 +
## vertical1 + ATL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - cold_weather 1 0.1 4002.0 -52878
## - CAR 1 0.1 4002.1 -52878
## - MIA 1 0.1 4002.1 -52878
## - SEA 1 0.1 4002.1 -52878
## - WAS 1 0.1 4002.1 -52878
## - OAK 1 0.1 4002.1 -52878
## - NYJ 1 0.2 4002.2 -52877
## - STL 1 0.2 4002.2 -52877
## - KC 1 0.2 4002.2 -52877
## - JAC 1 0.2 4002.2 -52877
## - PHI 1 0.3 4002.2 -52877
## - home_team_1 1 0.3 4002.3 -52877
## <none> 4002.0 -52877
## - MINN 1 0.4 4002.3 -52876
## - DET 1 0.6 4002.6 -52875
## - IND 1 0.6 4002.6 -52874
## - TEN 1 0.7 4002.7 -52874
## - CIN 1 0.8 4002.8 -52873
## - TB 1 1.0 4003.0 -52872
## - HOU 1 1.0 4003.0 -52872
## - DEN 1 1.2 4003.2 -52870
## - PIT 1 1.3 4003.3 -52869
## - CLE 1 1.4 4003.4 -52869
## - ATL 1 1.6 4003.6 -52868
## - CHI 1 1.7 4003.7 -52867
## - NYG 1 3.1 4005.1 -52857
## - avg_rbry_pos 1 3.2 4005.2 -52857
## - forty1 1 4.3 4006.2 -52849
## - vertical1 1 4.4 4006.4 -52848
## - NOR 1 5.3 4007.3 -52842
## - DAL 1 5.4 4007.4 -52842
## - SD 1 6.8 4008.8 -52832
## - avg_rectd_plyr 1 6.9 4008.8 -52831
## - NE 1 7.7 4009.7 -52825
## - GB 1 10.6 4012.6 -52806
## - weight 1 11.2 4013.2 -52801
## - avg_rbry_plyr 1 13.3 4015.3 -52787
## - height 1 25.4 4027.4 -52705
## - avg_fuml_plyr 1 130.0 4132.0 -52000
## - avg_qbtdp_plyr 1 7226.8 11228.8 -24524
##
## Step: AIC=-52878.17
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL +
## CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND +
## JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI +
## PIT + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - CAR 1 0.1 4002.1 -52879
## - MIA 1 0.1 4002.2 -52879
## - OAK 1 0.1 4002.2 -52879
## - WAS 1 0.1 4002.2 -52879
## - SEA 1 0.1 4002.2 -52879
## - NYJ 1 0.2 4002.2 -52879
## - STL 1 0.2 4002.2 -52879
## - KC 1 0.2 4002.3 -52879
## - JAC 1 0.2 4002.3 -52878
## - PHI 1 0.3 4002.3 -52878
## <none> 4002.0 -52878
## - home_team_1 1 0.3 4002.3 -52878
## - MINN 1 0.4 4002.4 -52878
## - DET 1 0.6 4002.6 -52876
## - IND 1 0.6 4002.7 -52876
## - TEN 1 0.7 4002.7 -52876
## - CIN 1 0.8 4002.9 -52875
## - TB 1 1.0 4003.0 -52873
## - HOU 1 1.1 4003.1 -52873
## - DEN 1 1.2 4003.3 -52872
## - CLE 1 1.4 4003.4 -52871
## - PIT 1 1.4 4003.4 -52871
## - ATL 1 1.6 4003.6 -52869
## - CHI 1 1.7 4003.8 -52868
## - avg_rbry_pos 1 3.2 4005.2 -52858
## - NYG 1 3.2 4005.2 -52858
## - forty1 1 4.3 4006.3 -52851
## - vertical1 1 4.4 4006.5 -52850
## - NOR 1 5.3 4007.3 -52844
## - DAL 1 5.4 4007.4 -52843
## - SD 1 6.8 4008.8 -52834
## - avg_rectd_plyr 1 6.9 4008.9 -52833
## - NE 1 7.9 4009.9 -52826
## - GB 1 10.7 4012.8 -52806
## - weight 1 11.3 4013.3 -52803
## - avg_rbry_plyr 1 13.3 4015.3 -52789
## - height 1 25.5 4027.5 -52706
## - avg_fuml_plyr 1 130.1 4132.1 -52001
## - avg_qbtdp_plyr 1 7226.8 11228.8 -24525
##
## Step: AIC=-52879.46
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT +
## SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.1 4002.2 -52881
## - OAK 1 0.1 4002.2 -52881
## - SEA 1 0.1 4002.2 -52881
## - NYJ 1 0.2 4002.3 -52880
## - WAS 1 0.2 4002.3 -52880
## - STL 1 0.3 4002.4 -52880
## <none> 4002.1 -52879
## - KC 1 0.3 4002.4 -52879
## - home_team_1 1 0.3 4002.5 -52879
## - JAC 1 0.3 4002.5 -52879
## - PHI 1 0.3 4002.5 -52879
## - MINN 1 0.5 4002.6 -52878
## - DET 1 0.5 4002.6 -52878
## - IND 1 0.6 4002.7 -52878
## - TEN 1 0.6 4002.7 -52877
## - CIN 1 0.7 4002.9 -52876
## - TB 1 0.9 4003.0 -52875
## - DEN 1 1.1 4003.3 -52874
## - HOU 1 1.2 4003.4 -52873
## - PIT 1 1.3 4003.4 -52873
## - ATL 1 1.5 4003.6 -52871
## - CLE 1 1.6 4003.7 -52871
## - CHI 1 1.6 4003.8 -52870
## - NYG 1 3.1 4005.2 -52860
## - avg_rbry_pos 1 3.2 4005.4 -52859
## - forty1 1 4.3 4006.4 -52852
## - vertical1 1 4.5 4006.6 -52851
## - NOR 1 5.2 4007.3 -52846
## - DAL 1 5.3 4007.4 -52845
## - SD 1 6.7 4008.9 -52835
## - avg_rectd_plyr 1 6.8 4009.0 -52834
## - NE 1 7.8 4009.9 -52828
## - GB 1 10.8 4012.9 -52808
## - weight 1 11.4 4013.5 -52804
## - avg_rbry_plyr 1 13.4 4015.5 -52790
## - height 1 25.6 4027.7 -52706
## - avg_fuml_plyr 1 130.1 4132.2 -52002
## - avg_qbtdp_plyr 1 7228.0 11230.2 -24524
##
## Step: AIC=-52880.83
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.1 4002.3 -52882
## - SEA 1 0.1 4002.3 -52882
## - NYJ 1 0.1 4002.4 -52882
## - WAS 1 0.2 4002.5 -52881
## <none> 4002.2 -52881
## - home_team_1 1 0.3 4002.6 -52881
## - STL 1 0.3 4002.6 -52881
## - KC 1 0.4 4002.6 -52880
## - JAC 1 0.4 4002.6 -52880
## - PHI 1 0.4 4002.6 -52880
## - DET 1 0.4 4002.7 -52880
## - IND 1 0.5 4002.7 -52879
## - TEN 1 0.5 4002.8 -52879
## - MINN 1 0.5 4002.8 -52879
## - CIN 1 0.7 4002.9 -52878
## - TB 1 0.8 4003.1 -52877
## - DEN 1 1.1 4003.3 -52876
## - PIT 1 1.2 4003.5 -52874
## - HOU 1 1.4 4003.6 -52873
## - ATL 1 1.4 4003.6 -52873
## - CHI 1 1.6 4003.8 -52872
## - CLE 1 1.7 4004.0 -52871
## - NYG 1 3.0 4005.2 -52862
## - avg_rbry_pos 1 3.2 4005.4 -52861
## - forty1 1 4.2 4006.5 -52854
## - vertical1 1 4.4 4006.7 -52852
## - NOR 1 5.1 4007.3 -52848
## - DAL 1 5.2 4007.4 -52847
## - SD 1 6.6 4008.9 -52837
## - avg_rectd_plyr 1 6.9 4009.1 -52836
## - NE 1 7.7 4010.0 -52830
## - GB 1 10.7 4013.0 -52809
## - weight 1 11.3 4013.6 -52805
## - avg_rbry_plyr 1 13.3 4015.6 -52791
## - height 1 25.6 4027.8 -52708
## - avg_fuml_plyr 1 130.0 4132.2 -52004
## - avg_qbtdp_plyr 1 7230.4 11232.6 -24520
##
## Step: AIC=-52882.36
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.1 4002.4 -52884
## - NYJ 1 0.1 4002.4 -52884
## - WAS 1 0.3 4002.6 -52882
## <none> 4002.3 -52882
## - home_team_1 1 0.3 4002.6 -52882
## - STL 1 0.4 4002.7 -52882
## - DET 1 0.4 4002.7 -52882
## - KC 1 0.4 4002.7 -52881
## - JAC 1 0.4 4002.8 -52881
## - IND 1 0.5 4002.8 -52881
## - PHI 1 0.5 4002.8 -52881
## - TEN 1 0.5 4002.8 -52881
## - MINN 1 0.6 4002.9 -52880
## - CIN 1 0.6 4002.9 -52880
## - TB 1 0.8 4003.1 -52879
## - DEN 1 1.0 4003.3 -52877
## - PIT 1 1.2 4003.5 -52876
## - ATL 1 1.3 4003.6 -52875
## - HOU 1 1.5 4003.8 -52874
## - CHI 1 1.5 4003.8 -52874
## - CLE 1 1.9 4004.2 -52871
## - NYG 1 2.9 4005.2 -52864
## - avg_rbry_pos 1 3.2 4005.5 -52863
## - forty1 1 4.3 4006.6 -52855
## - vertical1 1 4.4 4006.7 -52854
## - NOR 1 5.0 4007.3 -52850
## - DAL 1 5.1 4007.4 -52849
## - SD 1 6.6 4008.9 -52839
## - avg_rectd_plyr 1 6.9 4009.2 -52837
## - NE 1 7.7 4010.0 -52832
## - GB 1 10.7 4013.0 -52811
## - weight 1 11.3 4013.6 -52807
## - avg_rbry_plyr 1 13.3 4015.6 -52793
## - height 1 25.5 4027.8 -52710
## - avg_fuml_plyr 1 130.2 4132.5 -52005
## - avg_qbtdp_plyr 1 7230.3 11232.6 -24522
##
## Step: AIC=-52883.97
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## - NYJ 1 0.1 4002.4 -52885
## <none> 4002.4 -52884
## - WAS 1 0.3 4002.7 -52884
## - home_team_1 1 0.3 4002.7 -52884
## - DET 1 0.4 4002.7 -52883
## - IND 1 0.4 4002.8 -52883
## - STL 1 0.4 4002.8 -52883
## - TEN 1 0.5 4002.8 -52883
## - KC 1 0.5 4002.8 -52883
## - JAC 1 0.5 4002.9 -52883
## - PHI 1 0.5 4002.9 -52882
## - CIN 1 0.6 4002.9 -52882
## - MINN 1 0.7 4003.0 -52881
## - TB 1 0.7 4003.1 -52881
## - DEN 1 1.0 4003.3 -52879
## - PIT 1 1.1 4003.5 -52878
## - ATL 1 1.3 4003.6 -52877
## - CHI 1 1.5 4003.8 -52876
## - HOU 1 1.6 4004.0 -52875
## - CLE 1 2.0 4004.4 -52872
## - NYG 1 2.9 4005.2 -52866
## - avg_rbry_pos 1 3.2 4005.6 -52864
## - forty1 1 4.3 4006.6 -52857
## - vertical1 1 4.4 4006.8 -52855
## - NOR 1 5.0 4007.3 -52852
## - DAL 1 5.1 4007.4 -52851
## - SD 1 6.5 4008.9 -52841
## - avg_rectd_plyr 1 6.9 4009.2 -52839
## - NE 1 7.7 4010.0 -52833
## - GB 1 10.7 4013.1 -52812
## - weight 1 11.3 4013.7 -52808
## - avg_rbry_plyr 1 13.4 4015.7 -52794
## - height 1 25.7 4028.1 -52710
## - avg_fuml_plyr 1 130.7 4133.0 -52003
## - avg_qbtdp_plyr 1 7246.9 11249.3 -24483
##
## Step: AIC=-52885.4
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## KC + MINN + NE + NOR + NYG + PHI + PIT + SD + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr
##
## Df Sum of Sq RSS AIC
## <none> 4002.4 -52885
## - DET 1 0.3 4002.8 -52885
## - home_team_1 1 0.3 4002.8 -52885
## - WAS 1 0.4 4002.8 -52885
## - IND 1 0.4 4002.8 -52885
## - TEN 1 0.4 4002.9 -52885
## - STL 1 0.5 4002.9 -52884
## - KC 1 0.5 4003.0 -52884
## - CIN 1 0.5 4003.0 -52884
## - JAC 1 0.6 4003.0 -52884
## - PHI 1 0.6 4003.0 -52883
## - TB 1 0.7 4003.1 -52883
## - MINN 1 0.7 4003.2 -52882
## - DEN 1 0.9 4003.4 -52881
## - PIT 1 1.1 4003.5 -52880
## - ATL 1 1.2 4003.7 -52879
## - CHI 1 1.4 4003.8 -52878
## - HOU 1 1.7 4004.1 -52876
## - CLE 1 2.1 4004.6 -52873
## - NYG 1 2.8 4005.2 -52868
## - avg_rbry_pos 1 3.2 4005.7 -52865
## - forty1 1 4.2 4006.7 -52858
## - vertical1 1 4.6 4007.0 -52856
## - NOR 1 4.9 4007.4 -52854
## - DAL 1 5.0 4007.4 -52853
## - SD 1 6.4 4008.9 -52843
## - avg_rectd_plyr 1 6.9 4009.3 -52840
## - NE 1 7.6 4010.0 -52835
## - GB 1 10.6 4013.1 -52814
## - weight 1 11.3 4013.7 -52810
## - avg_rbry_plyr 1 13.4 4015.9 -52795
## - height 1 25.7 4028.2 -52711
## - avg_fuml_plyr 1 130.6 4133.1 -52005
## - avg_qbtdp_plyr 1 7256.2 11258.6 -24463Rushing Stats
Rushing Yards
PreProcess:
set.seed(123)
splitry <- sample.split(nfl_data$ry, SplitRatio = 0.7)
Trainry <- subset(nfl_data, split == TRUE)
Testry <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainry, method = c("center", "scale"))
trainTransformedry <- predict(preProcValues, Trainry)
testTransformedry <- predict(preProcValues, Testry)ggpairs:
ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[46:51]))])
ryregform <- formula(paste("ry ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegRushYd <- lm(ryregform, data = trainTransformedry)
summary(linRegRushYd)##
## Call:
## lm(formula = ryregform, data = trainTransformedry)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4869 -0.0828 -0.0119 0.0246 7.1651
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.344e-14 3.913e-03 0.000 1.000000
## height -2.408e-03 7.592e-03 -0.317 0.751079
## weight 1.953e-03 7.115e-03 0.275 0.783686
## cold_weather 1.400e-02 4.119e-03 3.399 0.000678 ***
## hot_weather -1.387e-03 3.949e-03 -0.351 0.725333
## home_team_1 1.003e-02 4.257e-03 2.357 0.018453 *
## forty1 -1.549e-03 6.753e-03 -0.229 0.818571
## vertical1 -1.878e-03 5.192e-03 -0.362 0.717597
## ARI 4.434e-04 5.473e-03 0.081 0.935433
## ATL 5.374e-04 5.500e-03 0.098 0.922157
## BAL -2.362e-03 5.504e-03 -0.429 0.667904
## BUF -1.553e-03 5.434e-03 -0.286 0.774986
## CAR -6.492e-03 5.398e-03 -1.203 0.229179
## CHI -2.772e-03 5.338e-03 -0.519 0.603544
## CIN -7.663e-04 5.436e-03 -0.141 0.887901
## CLE 2.003e-03 5.411e-03 0.370 0.711216
## DAL 1.735e-03 5.466e-03 0.317 0.750989
## DEN 6.652e-03 5.487e-03 1.212 0.225401
## DET 3.673e-03 5.411e-03 0.679 0.497292
## GB -4.934e-03 5.571e-03 -0.886 0.375822
## HOU 5.347e-03 5.505e-03 0.971 0.331381
## IND -4.118e-03 5.465e-03 -0.754 0.451137
## JAC -1.431e-03 5.330e-03 -0.268 0.788321
## KC 2.573e-04 5.447e-03 0.047 0.962318
## MIA 2.191e-03 5.360e-03 0.409 0.682622
## MINN -1.518e-03 5.392e-03 -0.282 0.778260
## NE -1.918e-03 5.632e-03 -0.341 0.733407
## NOR -7.365e-03 5.614e-03 -1.312 0.189568
## NYG 3.399e-03 5.488e-03 0.619 0.535628
## NYJ -6.759e-03 5.467e-03 -1.236 0.216349
## OAK 3.653e-04 5.502e-03 0.066 0.947061
## PHI -2.417e-03 5.331e-03 -0.453 0.650336
## PIT -6.720e-03 5.471e-03 -1.228 0.219398
## SD -2.446e-03 5.369e-03 -0.456 0.648733
## SEA -5.358e-03 5.572e-03 -0.961 0.336316
## STL 3.688e-03 5.423e-03 0.680 0.496463
## TB 7.938e-04 5.372e-03 0.148 0.882546
## TEN 2.142e-03 5.405e-03 0.396 0.691874
## WAS 5.495e-03 5.434e-03 1.011 0.311876
## avg_trg_team NA NA NA NA
## avg_rectd_plyr 2.091e-03 4.997e-03 0.418 0.675637
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr 7.585e-01 5.980e-03 126.854 < 2e-16 ***
## avg_rbry_pos 3.452e-03 6.967e-03 0.495 0.620259
## avg_fuml_plyr 7.112e-04 5.780e-03 0.123 0.902077
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -2.003e-06 6.279e-03 0.000 0.999745
## avg_qbtdp_team NA NA NA NA
## grass_1 -7.838e-03 4.502e-03 -1.741 0.081702 .
## bad_weather_1 6.390e-03 3.980e-03 1.605 0.108436
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6487 on 27438 degrees of freedom
## Multiple R-squared: 0.5799, Adjusted R-squared: 0.5792
## F-statistic: 841.6 on 45 and 27438 DF, p-value: < 2.2e-16linRegRushYd2 <- update(linRegRushYd,~.-height-weight-hot_weather-home_team_1-is_WR-is_TE-forty1
-vertical1-ARI-ATL-BAL - BUF - CAR - CHI
-CIN - CLE - DAL - DEN - DET - GB - HOU - IND - JAC - KC - MIA
-MINN - NE - NOR - NYG-NYJ - OAK - PHI - PIT -SD - SEA - STL
-TB - TEN - WAS
-avg_rectd_plyr-avg_trg_team-avg_tdr_team-avg_rbra_team-avg_rbry_pos
-avg_fuml_team-avg_fuml_plyr-avg_qbints_team-avg_qbtdp_team
-avg_qbints_plyr-bad_weather_1-grass_1)
summary(linRegRushYd2)##
## Call:
## lm(formula = ry ~ cold_weather + avg_rbry_plyr + avg_qbtdp_plyr,
## data = trainTransformedry)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4564 -0.0775 -0.0072 0.0077 7.1706
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.343e-14 3.913e-03 0.000 1.000000
## cold_weather 1.409e-02 3.913e-03 3.602 0.000316 ***
## avg_rbry_plyr 7.609e-01 3.913e-03 194.477 < 2e-16 ***
## avg_qbtdp_plyr -1.208e-03 3.913e-03 -0.309 0.757571
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6486 on 27480 degrees of freedom
## Multiple R-squared: 0.5793, Adjusted R-squared: 0.5793
## F-statistic: 1.261e+04 on 3 and 27480 DF, p-value: < 2.2e-16Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
RushydsPredicted <- predict(linRegRushYd2, newdata = testTransformedry)
SSEruyd <- sum((RushydsPredicted - testTransformedry$ry)^2)
SSTruyd <- sum((mean(nfl_data$ry)-testTransformedry$ry)^2)
r2_ruyd <- 1 - SSEruyd/SSTruyd
r2_ruyd## [1] 0.996394rmse_ruyd <- sqrt(SSEruyd/nrow(testTransformedry))
rmse_ruyd## [1] 0.6467476Regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegRushYd2, which = c(1:3,5))
Summary statistics:
confint(linRegRushYd2)## 2.5 % 97.5 %
## (Intercept) -0.007668979 0.007668979
## cold_weather 0.006424438 0.021762752
## avg_rbry_plyr 0.753270275 0.768608611
## avg_qbtdp_plyr -0.008876890 0.006461374coef(summary(linRegRushYd2))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.343374e-14 0.003912644 5.989234e-12 1.0000000000
## cold_weather 1.409359e-02 0.003912735 3.601981e+00 0.0003163587
## avg_rbry_plyr 7.609394e-01 0.003912740 1.944774e+02 0.0000000000
## avg_qbtdp_plyr -1.207758e-03 0.003912722 -3.086747e-01 0.7575713455anova(linRegRushYd2)## Analysis of Variance Table
##
## Response: ry
## Df Sum Sq Mean Sq F value Pr(>F)
## cold_weather 1 7.5 7.5 17.7329 2.55e-05 ***
## avg_rbry_plyr 1 15913.4 15913.4 37821.7831 < 2.2e-16 ***
## avg_qbtdp_plyr 1 0.0 0.0 0.0953 0.7576
## Residuals 27480 11562.1 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_ry <- step(lm(ryregform, data = trainTransformedry), direction = "backward")## Start: AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_qbtdp_plyr 1 0.0 11546 -23746
## - KC 1 0.0 11546 -23746
## - OAK 1 0.0 11546 -23746
## - ARI 1 0.0 11546 -23746
## - ATL 1 0.0 11546 -23746
## - avg_fuml_plyr 1 0.0 11546 -23746
## - CIN 1 0.0 11546 -23746
## - TB 1 0.0 11546 -23746
## - forty1 1 0.0 11546 -23746
## - JAC 1 0.0 11546 -23746
## - weight 1 0.0 11546 -23746
## - MINN 1 0.0 11546 -23746
## - BUF 1 0.0 11546 -23746
## - height 1 0.0 11546 -23746
## - DAL 1 0.0 11546 -23746
## - NE 1 0.0 11546 -23746
## - hot_weather 1 0.1 11546 -23746
## - vertical1 1 0.1 11546 -23746
## - CLE 1 0.1 11546 -23746
## - TEN 1 0.1 11546 -23746
## - MIA 1 0.1 11546 -23746
## - avg_rectd_plyr 1 0.1 11546 -23746
## - BAL 1 0.1 11546 -23746
## - PHI 1 0.1 11546 -23746
## - SD 1 0.1 11546 -23746
## - avg_rbry_pos 1 0.1 11546 -23746
## - CHI 1 0.1 11546 -23746
## - NYG 1 0.2 11546 -23746
## - DET 1 0.2 11546 -23746
## - STL 1 0.2 11546 -23746
## - IND 1 0.2 11546 -23745
## - GB 1 0.3 11546 -23745
## - SEA 1 0.4 11546 -23745
## - HOU 1 0.4 11546 -23745
## - WAS 1 0.4 11546 -23745
## - CAR 1 0.6 11547 -23745
## - DEN 1 0.6 11547 -23745
## - PIT 1 0.6 11547 -23745
## - NYJ 1 0.6 11547 -23745
## - NOR 1 0.7 11547 -23744
## <none> 11546 -23744
## - bad_weather_1 1 1.1 11547 -23743
## - grass_1 1 1.3 11547 -23743
## - home_team_1 1 2.3 11548 -23740
## - cold_weather 1 4.9 11551 -23734
## - avg_rbry_plyr 1 6771.6 18318 -11062
##
## Step: AIC=-23746.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - KC 1 0.0 11546 -23748
## - OAK 1 0.0 11546 -23748
## - ARI 1 0.0 11546 -23748
## - ATL 1 0.0 11546 -23748
## - CIN 1 0.0 11546 -23748
## - TB 1 0.0 11546 -23748
## - avg_fuml_plyr 1 0.0 11546 -23748
## - forty1 1 0.0 11546 -23748
## - JAC 1 0.0 11546 -23748
## - MINN 1 0.0 11546 -23748
## - weight 1 0.0 11546 -23748
## - BUF 1 0.0 11546 -23748
## - DAL 1 0.0 11546 -23748
## - height 1 0.0 11546 -23748
## - NE 1 0.0 11546 -23748
## - hot_weather 1 0.1 11546 -23748
## - vertical1 1 0.1 11546 -23748
## - CLE 1 0.1 11546 -23748
## - TEN 1 0.1 11546 -23748
## - MIA 1 0.1 11546 -23748
## - BAL 1 0.1 11546 -23748
## - avg_rectd_plyr 1 0.1 11546 -23748
## - PHI 1 0.1 11546 -23748
## - SD 1 0.1 11546 -23748
## - avg_rbry_pos 1 0.1 11546 -23748
## - CHI 1 0.1 11546 -23748
## - NYG 1 0.2 11546 -23748
## - DET 1 0.2 11546 -23748
## - STL 1 0.2 11546 -23748
## - IND 1 0.2 11546 -23747
## - GB 1 0.3 11546 -23747
## - SEA 1 0.4 11546 -23747
## - HOU 1 0.4 11546 -23747
## - WAS 1 0.4 11546 -23747
## - CAR 1 0.6 11547 -23747
## - DEN 1 0.6 11547 -23747
## - PIT 1 0.6 11547 -23747
## - NYJ 1 0.6 11547 -23747
## - NOR 1 0.7 11547 -23746
## <none> 11546 -23746
## - bad_weather_1 1 1.1 11547 -23745
## - grass_1 1 1.3 11547 -23745
## - home_team_1 1 2.3 11548 -23742
## - cold_weather 1 4.9 11551 -23736
## - avg_rbry_plyr 1 6897.6 18444 -10875
##
## Step: AIC=-23748.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.0 11546 -23750
## - ARI 1 0.0 11546 -23750
## - ATL 1 0.0 11546 -23750
## - TB 1 0.0 11546 -23750
## - avg_fuml_plyr 1 0.0 11546 -23750
## - CIN 1 0.0 11546 -23750
## - forty1 1 0.0 11546 -23750
## - weight 1 0.0 11546 -23750
## - height 1 0.0 11546 -23750
## - JAC 1 0.0 11546 -23750
## - DAL 1 0.0 11546 -23750
## - MINN 1 0.1 11546 -23750
## - hot_weather 1 0.1 11546 -23750
## - BUF 1 0.1 11546 -23750
## - vertical1 1 0.1 11546 -23750
## - CLE 1 0.1 11546 -23750
## - NE 1 0.1 11546 -23750
## - avg_rectd_plyr 1 0.1 11546 -23750
## - TEN 1 0.1 11546 -23750
## - MIA 1 0.1 11546 -23750
## - avg_rbry_pos 1 0.1 11546 -23750
## - BAL 1 0.1 11546 -23750
## - PHI 1 0.1 11546 -23750
## - SD 1 0.1 11546 -23750
## - CHI 1 0.2 11546 -23750
## - NYG 1 0.2 11546 -23750
## - DET 1 0.2 11546 -23749
## - STL 1 0.2 11546 -23749
## - IND 1 0.3 11546 -23749
## - GB 1 0.5 11546 -23749
## - HOU 1 0.5 11546 -23749
## - SEA 1 0.5 11546 -23749
## - WAS 1 0.5 11546 -23749
## - DEN 1 0.8 11547 -23748
## - CAR 1 0.8 11547 -23748
## <none> 11546 -23748
## - NYJ 1 0.9 11547 -23748
## - PIT 1 0.9 11547 -23748
## - NOR 1 1.0 11547 -23748
## - bad_weather_1 1 1.1 11547 -23747
## - grass_1 1 1.3 11547 -23747
## - home_team_1 1 2.3 11548 -23744
## - cold_weather 1 4.9 11551 -23738
## - avg_rbry_plyr 1 6898.0 18444 -10876
##
## Step: AIC=-23750
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ARI 1 0.0 11546 -23752
## - ATL 1 0.0 11546 -23752
## - TB 1 0.0 11546 -23752
## - avg_fuml_plyr 1 0.0 11546 -23752
## - CIN 1 0.0 11546 -23752
## - forty1 1 0.0 11546 -23752
## - weight 1 0.0 11546 -23752
## - height 1 0.0 11546 -23752
## - DAL 1 0.0 11546 -23752
## - hot_weather 1 0.1 11546 -23752
## - vertical1 1 0.1 11546 -23752
## - JAC 1 0.1 11546 -23752
## - MINN 1 0.1 11546 -23752
## - BUF 1 0.1 11546 -23752
## - CLE 1 0.1 11546 -23752
## - avg_rectd_plyr 1 0.1 11546 -23752
## - TEN 1 0.1 11546 -23752
## - MIA 1 0.1 11546 -23752
## - NE 1 0.1 11546 -23752
## - avg_rbry_pos 1 0.1 11546 -23752
## - BAL 1 0.1 11546 -23752
## - PHI 1 0.1 11546 -23752
## - SD 1 0.1 11546 -23752
## - CHI 1 0.2 11546 -23752
## - NYG 1 0.2 11546 -23752
## - DET 1 0.3 11546 -23751
## - STL 1 0.3 11546 -23751
## - IND 1 0.4 11546 -23751
## - HOU 1 0.5 11546 -23751
## - GB 1 0.5 11546 -23751
## - WAS 1 0.6 11547 -23751
## - SEA 1 0.6 11547 -23751
## <none> 11546 -23750
## - DEN 1 0.9 11547 -23750
## - CAR 1 1.0 11547 -23750
## - NYJ 1 1.0 11547 -23750
## - PIT 1 1.0 11547 -23750
## - bad_weather_1 1 1.1 11547 -23749
## - NOR 1 1.1 11547 -23749
## - grass_1 1 1.3 11547 -23749
## - home_team_1 1 2.3 11548 -23746
## - cold_weather 1 4.9 11551 -23740
## - avg_rbry_plyr 1 6907.2 18453 -10865
##
## Step: AIC=-23752
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ATL + BAL + BUF + CAR + CHI + CIN +
## CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN +
## NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - ATL 1 0.0 11546 -23754
## - TB 1 0.0 11546 -23754
## - avg_fuml_plyr 1 0.0 11546 -23754
## - CIN 1 0.0 11546 -23754
## - forty1 1 0.0 11546 -23754
## - weight 1 0.0 11546 -23754
## - height 1 0.0 11546 -23754
## - DAL 1 0.0 11546 -23754
## - hot_weather 1 0.1 11546 -23754
## - vertical1 1 0.1 11546 -23754
## - JAC 1 0.1 11546 -23754
## - CLE 1 0.1 11546 -23754
## - MINN 1 0.1 11546 -23754
## - BUF 1 0.1 11546 -23754
## - avg_rectd_plyr 1 0.1 11546 -23754
## - TEN 1 0.1 11546 -23754
## - MIA 1 0.1 11546 -23754
## - NE 1 0.1 11546 -23754
## - avg_rbry_pos 1 0.1 11546 -23754
## - BAL 1 0.2 11546 -23754
## - PHI 1 0.2 11546 -23754
## - SD 1 0.2 11546 -23754
## - CHI 1 0.2 11546 -23754
## - NYG 1 0.2 11546 -23754
## - DET 1 0.3 11546 -23753
## - STL 1 0.3 11546 -23753
## - IND 1 0.4 11546 -23753
## - HOU 1 0.6 11546 -23753
## - GB 1 0.6 11547 -23753
## - WAS 1 0.6 11547 -23753
## - SEA 1 0.7 11547 -23752
## <none> 11546 -23752
## - DEN 1 0.9 11547 -23752
## - CAR 1 1.0 11547 -23752
## - bad_weather_1 1 1.1 11547 -23751
## - NYJ 1 1.1 11547 -23751
## - PIT 1 1.1 11547 -23751
## - NOR 1 1.3 11547 -23751
## - grass_1 1 1.3 11547 -23751
## - home_team_1 1 2.4 11548 -23748
## - cold_weather 1 4.9 11551 -23742
## - avg_rbry_plyr 1 6911.8 18458 -10860
##
## Step: AIC=-23754
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE +
## NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TB 1 0.0 11546 -23756
## - avg_fuml_plyr 1 0.0 11546 -23756
## - forty1 1 0.0 11546 -23756
## - CIN 1 0.0 11546 -23756
## - weight 1 0.0 11546 -23756
## - height 1 0.0 11546 -23756
## - DAL 1 0.0 11546 -23756
## - hot_weather 1 0.1 11546 -23756
## - vertical1 1 0.1 11546 -23756
## - CLE 1 0.1 11546 -23756
## - JAC 1 0.1 11546 -23756
## - MINN 1 0.1 11546 -23756
## - avg_rectd_plyr 1 0.1 11546 -23756
## - TEN 1 0.1 11546 -23756
## - BUF 1 0.1 11546 -23756
## - MIA 1 0.1 11546 -23756
## - avg_rbry_pos 1 0.1 11546 -23756
## - NE 1 0.1 11546 -23756
## - BAL 1 0.2 11546 -23756
## - PHI 1 0.2 11546 -23756
## - SD 1 0.2 11546 -23756
## - NYG 1 0.2 11546 -23756
## - CHI 1 0.2 11546 -23756
## - DET 1 0.3 11546 -23755
## - STL 1 0.3 11546 -23755
## - IND 1 0.5 11546 -23755
## - HOU 1 0.6 11546 -23755
## - WAS 1 0.6 11547 -23755
## - GB 1 0.6 11547 -23755
## - SEA 1 0.7 11547 -23754
## <none> 11546 -23754
## - DEN 1 0.9 11547 -23754
## - bad_weather_1 1 1.1 11547 -23753
## - CAR 1 1.1 11547 -23753
## - PIT 1 1.1 11547 -23753
## - NYJ 1 1.1 11547 -23753
## - grass_1 1 1.3 11547 -23753
## - NOR 1 1.4 11547 -23753
## - home_team_1 1 2.4 11548 -23750
## - cold_weather 1 4.9 11551 -23744
## - avg_rbry_plyr 1 6912.0 18458 -10862
##
## Step: AIC=-23755.98
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE +
## NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_fuml_plyr 1 0.0 11546 -23758
## - forty1 1 0.0 11546 -23758
## - CIN 1 0.0 11546 -23758
## - weight 1 0.0 11546 -23758
## - DAL 1 0.0 11546 -23758
## - height 1 0.0 11546 -23758
## - hot_weather 1 0.1 11546 -23758
## - vertical1 1 0.1 11546 -23758
## - CLE 1 0.1 11546 -23758
## - TEN 1 0.1 11546 -23758
## - avg_rectd_plyr 1 0.1 11546 -23758
## - JAC 1 0.1 11546 -23758
## - MIA 1 0.1 11546 -23758
## - MINN 1 0.1 11546 -23758
## - BUF 1 0.1 11546 -23758
## - avg_rbry_pos 1 0.1 11546 -23758
## - NE 1 0.1 11546 -23758
## - BAL 1 0.2 11546 -23758
## - PHI 1 0.2 11546 -23758
## - SD 1 0.2 11546 -23758
## - NYG 1 0.2 11546 -23758
## - CHI 1 0.2 11546 -23757
## - DET 1 0.3 11546 -23757
## - STL 1 0.3 11546 -23757
## - IND 1 0.5 11546 -23757
## - HOU 1 0.6 11546 -23757
## - WAS 1 0.6 11547 -23757
## - GB 1 0.7 11547 -23756
## - SEA 1 0.8 11547 -23756
## <none> 11546 -23756
## - DEN 1 0.9 11547 -23756
## - bad_weather_1 1 1.1 11547 -23755
## - CAR 1 1.1 11547 -23755
## - PIT 1 1.2 11547 -23755
## - NYJ 1 1.2 11547 -23755
## - grass_1 1 1.3 11547 -23755
## - NOR 1 1.4 11547 -23755
## - home_team_1 1 2.4 11548 -23752
## - cold_weather 1 4.9 11551 -23746
## - avg_rbry_plyr 1 6912.0 18458 -10864
##
## Step: AIC=-23757.96
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE +
## NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - forty1 1 0.0 11546 -23759.9
## - weight 1 0.0 11546 -23759.9
## - CIN 1 0.0 11546 -23759.9
## - height 1 0.0 11546 -23759.9
## - DAL 1 0.0 11546 -23759.9
## - hot_weather 1 0.1 11546 -23759.8
## - vertical1 1 0.1 11546 -23759.8
## - CLE 1 0.1 11546 -23759.8
## - avg_rectd_plyr 1 0.1 11546 -23759.8
## - TEN 1 0.1 11546 -23759.8
## - JAC 1 0.1 11546 -23759.8
## - MIA 1 0.1 11546 -23759.8
## - MINN 1 0.1 11546 -23759.8
## - BUF 1 0.1 11546 -23759.7
## - avg_rbry_pos 1 0.1 11546 -23759.7
## - NE 1 0.1 11546 -23759.7
## - BAL 1 0.2 11546 -23759.5
## - PHI 1 0.2 11546 -23759.5
## - SD 1 0.2 11546 -23759.5
## - NYG 1 0.2 11546 -23759.5
## - CHI 1 0.2 11546 -23759.4
## - STL 1 0.3 11546 -23759.3
## - DET 1 0.3 11546 -23759.3
## - IND 1 0.5 11546 -23758.8
## - HOU 1 0.6 11547 -23758.6
## - WAS 1 0.6 11547 -23758.5
## - GB 1 0.7 11547 -23758.4
## - SEA 1 0.8 11547 -23758.1
## <none> 11546 -23758.0
## - DEN 1 0.9 11547 -23757.7
## - bad_weather_1 1 1.1 11547 -23757.4
## - CAR 1 1.1 11547 -23757.2
## - PIT 1 1.2 11547 -23757.1
## - NYJ 1 1.2 11547 -23757.1
## - grass_1 1 1.3 11547 -23756.8
## - NOR 1 1.4 11547 -23756.6
## - home_team_1 1 2.4 11548 -23754.3
## - cold_weather 1 4.9 11551 -23748.4
## - avg_rbry_plyr 1 7680.5 19227 -9744.5
##
## Step: AIC=-23759.92
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 +
## vertical1 + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR + NYG +
## NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - weight 1 0.0 11546 -23761.9
## - CIN 1 0.0 11546 -23761.8
## - vertical1 1 0.0 11546 -23761.8
## - DAL 1 0.0 11546 -23761.8
## - height 1 0.0 11546 -23761.8
## - hot_weather 1 0.1 11546 -23761.8
## - CLE 1 0.1 11546 -23761.8
## - TEN 1 0.1 11546 -23761.7
## - MIA 1 0.1 11546 -23761.7
## - JAC 1 0.1 11546 -23761.7
## - BUF 1 0.1 11546 -23761.7
## - MINN 1 0.1 11546 -23761.7
## - avg_rectd_plyr 1 0.1 11546 -23761.7
## - avg_rbry_pos 1 0.1 11546 -23761.7
## - NE 1 0.1 11546 -23761.6
## - BAL 1 0.2 11546 -23761.5
## - PHI 1 0.2 11546 -23761.5
## - SD 1 0.2 11546 -23761.4
## - NYG 1 0.2 11546 -23761.4
## - CHI 1 0.2 11546 -23761.4
## - DET 1 0.3 11546 -23761.3
## - STL 1 0.3 11546 -23761.3
## - IND 1 0.5 11546 -23760.8
## - HOU 1 0.6 11547 -23760.6
## - WAS 1 0.6 11547 -23760.4
## - GB 1 0.7 11547 -23760.3
## - SEA 1 0.8 11547 -23760.1
## <none> 11546 -23759.9
## - DEN 1 0.9 11547 -23759.7
## - bad_weather_1 1 1.1 11547 -23759.3
## - CAR 1 1.1 11547 -23759.2
## - PIT 1 1.2 11547 -23759.0
## - NYJ 1 1.2 11547 -23759.0
## - grass_1 1 1.3 11547 -23758.8
## - NOR 1 1.4 11547 -23758.5
## - home_team_1 1 2.4 11548 -23756.2
## - cold_weather 1 4.9 11551 -23750.3
## - avg_rbry_plyr 1 7878.2 19424 -9465.3
##
## Step: AIC=-23761.88
## ry ~ height + cold_weather + hot_weather + home_team_1 + vertical1 +
## BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB +
## HOU + IND + JAC + MIA + MINN + NE + NOR + NYG + NYJ + PHI +
## PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - height 1 0.0 11546 -23763.8
## - CIN 1 0.0 11546 -23763.8
## - DAL 1 0.0 11546 -23763.8
## - vertical1 1 0.0 11546 -23763.8
## - hot_weather 1 0.1 11546 -23763.8
## - CLE 1 0.1 11546 -23763.7
## - TEN 1 0.1 11546 -23763.7
## - MIA 1 0.1 11546 -23763.7
## - JAC 1 0.1 11546 -23763.7
## - BUF 1 0.1 11546 -23763.7
## - MINN 1 0.1 11546 -23763.7
## - avg_rectd_plyr 1 0.1 11546 -23763.6
## - NE 1 0.1 11546 -23763.5
## - avg_rbry_pos 1 0.2 11546 -23763.5
## - BAL 1 0.2 11546 -23763.4
## - PHI 1 0.2 11546 -23763.4
## - SD 1 0.2 11546 -23763.4
## - NYG 1 0.2 11546 -23763.4
## - CHI 1 0.2 11546 -23763.3
## - DET 1 0.3 11546 -23763.3
## - STL 1 0.3 11546 -23763.3
## - IND 1 0.5 11546 -23762.7
## - HOU 1 0.6 11547 -23762.5
## - WAS 1 0.6 11547 -23762.3
## - GB 1 0.7 11547 -23762.3
## - SEA 1 0.8 11547 -23762.0
## <none> 11546 -23761.9
## - DEN 1 0.9 11547 -23761.7
## - bad_weather_1 1 1.1 11547 -23761.3
## - CAR 1 1.1 11547 -23761.2
## - PIT 1 1.2 11547 -23761.0
## - NYJ 1 1.2 11547 -23761.0
## - grass_1 1 1.3 11547 -23760.7
## - NOR 1 1.4 11547 -23760.5
## - home_team_1 1 2.4 11548 -23758.2
## - cold_weather 1 4.9 11551 -23752.3
## - avg_rbry_plyr 1 7904.9 19451 -9429.5
##
## Step: AIC=-23763.8
## ry ~ cold_weather + hot_weather + home_team_1 + vertical1 + BAL +
## BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU +
## IND + JAC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + PIT +
## SD + SEA + STL + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 0.0 11546 -23766
## - CIN 1 0.0 11546 -23766
## - DAL 1 0.0 11546 -23766
## - hot_weather 1 0.1 11546 -23766
## - CLE 1 0.1 11546 -23766
## - TEN 1 0.1 11546 -23766
## - MIA 1 0.1 11546 -23766
## - JAC 1 0.1 11546 -23766
## - BUF 1 0.1 11546 -23766
## - MINN 1 0.1 11546 -23766
## - avg_rectd_plyr 1 0.1 11546 -23766
## - NE 1 0.1 11546 -23766
## - PHI 1 0.2 11546 -23765
## - BAL 1 0.2 11546 -23765
## - NYG 1 0.2 11546 -23765
## - SD 1 0.2 11546 -23765
## - CHI 1 0.2 11546 -23765
## - avg_rbry_pos 1 0.3 11546 -23765
## - DET 1 0.3 11546 -23765
## - STL 1 0.3 11546 -23765
## - IND 1 0.5 11546 -23765
## - HOU 1 0.6 11547 -23765
## - WAS 1 0.7 11547 -23764
## - GB 1 0.7 11547 -23764
## - SEA 1 0.8 11547 -23764
## <none> 11546 -23764
## - DEN 1 0.9 11547 -23764
## - bad_weather_1 1 1.1 11547 -23763
## - CAR 1 1.1 11547 -23763
## - PIT 1 1.2 11547 -23763
## - NYJ 1 1.2 11547 -23763
## - grass_1 1 1.3 11547 -23763
## - NOR 1 1.4 11548 -23762
## - home_team_1 1 2.4 11548 -23760
## - cold_weather 1 4.9 11551 -23754
## - avg_rbry_plyr 1 7905.2 19451 -9431
##
## Step: AIC=-23765.73
## ry ~ cold_weather + hot_weather + home_team_1 + BAL + BUF + CAR +
## CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC +
## MIA + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA +
## STL + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CIN 1 0.0 11546 -23767.6
## - DAL 1 0.0 11546 -23767.6
## - hot_weather 1 0.1 11546 -23767.6
## - CLE 1 0.1 11546 -23767.6
## - TEN 1 0.1 11546 -23767.6
## - avg_rectd_plyr 1 0.1 11546 -23767.5
## - MIA 1 0.1 11546 -23767.5
## - JAC 1 0.1 11546 -23767.5
## - BUF 1 0.1 11546 -23767.5
## - MINN 1 0.1 11546 -23767.5
## - NE 1 0.1 11546 -23767.4
## - PHI 1 0.2 11546 -23767.3
## - BAL 1 0.2 11546 -23767.3
## - SD 1 0.2 11546 -23767.2
## - NYG 1 0.2 11546 -23767.2
## - CHI 1 0.2 11546 -23767.2
## - DET 1 0.2 11546 -23767.1
## - avg_rbry_pos 1 0.3 11546 -23767.1
## - STL 1 0.3 11546 -23767.1
## - IND 1 0.5 11547 -23766.6
## - HOU 1 0.6 11547 -23766.4
## - WAS 1 0.7 11547 -23766.2
## - GB 1 0.7 11547 -23766.2
## - SEA 1 0.8 11547 -23765.9
## <none> 11546 -23765.7
## - DEN 1 0.9 11547 -23765.5
## - bad_weather_1 1 1.1 11547 -23765.2
## - CAR 1 1.1 11547 -23765.0
## - PIT 1 1.2 11547 -23764.9
## - NYJ 1 1.2 11547 -23764.8
## - grass_1 1 1.3 11547 -23764.6
## - NOR 1 1.4 11548 -23764.3
## - home_team_1 1 2.4 11548 -23762.1
## - cold_weather 1 4.9 11551 -23756.1
## - avg_rbry_plyr 1 7918.4 19465 -9414.3
##
## Step: AIC=-23767.65
## ry ~ cold_weather + hot_weather + home_team_1 + BAL + BUF + CAR +
## CHI + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA +
## MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.1 11546 -23769.5
## - DAL 1 0.1 11546 -23769.5
## - CLE 1 0.1 11546 -23769.5
## - BUF 1 0.1 11546 -23769.5
## - JAC 1 0.1 11546 -23769.5
## - avg_rectd_plyr 1 0.1 11546 -23769.5
## - MINN 1 0.1 11546 -23769.4
## - TEN 1 0.1 11546 -23769.4
## - MIA 1 0.1 11546 -23769.4
## - NE 1 0.1 11546 -23769.4
## - BAL 1 0.2 11546 -23769.3
## - PHI 1 0.2 11546 -23769.3
## - SD 1 0.2 11546 -23769.2
## - CHI 1 0.2 11546 -23769.1
## - NYG 1 0.2 11546 -23769.1
## - avg_rbry_pos 1 0.3 11546 -23769.0
## - DET 1 0.3 11546 -23769.0
## - STL 1 0.3 11546 -23768.9
## - IND 1 0.5 11547 -23768.6
## - HOU 1 0.6 11547 -23768.2
## - GB 1 0.6 11547 -23768.1
## - WAS 1 0.7 11547 -23767.9
## - SEA 1 0.7 11547 -23767.9
## <none> 11546 -23767.6
## - DEN 1 1.0 11547 -23767.3
## - bad_weather_1 1 1.1 11547 -23767.1
## - CAR 1 1.1 11547 -23767.0
## - PIT 1 1.2 11547 -23766.9
## - NYJ 1 1.2 11547 -23766.8
## - grass_1 1 1.3 11547 -23766.6
## - NOR 1 1.4 11548 -23766.3
## - home_team_1 1 2.4 11548 -23764.0
## - cold_weather 1 4.8 11551 -23758.1
## - avg_rbry_plyr 1 7920.9 19467 -9412.7
##
## Step: AIC=-23769.52
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE +
## NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DAL 1 0.1 11546 -23771.4
## - JAC 1 0.1 11546 -23771.3
## - CLE 1 0.1 11546 -23771.3
## - BUF 1 0.1 11546 -23771.3
## - avg_rectd_plyr 1 0.1 11546 -23771.3
## - MINN 1 0.1 11546 -23771.3
## - TEN 1 0.1 11546 -23771.3
## - MIA 1 0.1 11546 -23771.3
## - NE 1 0.1 11546 -23771.3
## - PHI 1 0.2 11546 -23771.1
## - BAL 1 0.2 11546 -23771.1
## - SD 1 0.2 11546 -23771.1
## - CHI 1 0.2 11546 -23771.0
## - NYG 1 0.2 11546 -23770.9
## - avg_rbry_pos 1 0.3 11546 -23770.9
## - DET 1 0.3 11546 -23770.9
## - STL 1 0.3 11546 -23770.8
## - IND 1 0.5 11547 -23770.4
## - HOU 1 0.6 11547 -23770.1
## - GB 1 0.6 11547 -23770.0
## - WAS 1 0.7 11547 -23769.8
## - SEA 1 0.8 11547 -23769.7
## <none> 11546 -23769.5
## - DEN 1 1.0 11547 -23769.2
## - bad_weather_1 1 1.1 11547 -23769.0
## - CAR 1 1.1 11547 -23768.9
## - PIT 1 1.2 11547 -23768.7
## - NYJ 1 1.2 11547 -23768.6
## - grass_1 1 1.3 11548 -23768.3
## - NOR 1 1.4 11548 -23768.2
## - home_team_1 1 2.4 11548 -23765.9
## - cold_weather 1 4.9 11551 -23759.9
## - avg_rbry_plyr 1 7921.2 19467 -9414.3
##
## Step: AIC=-23771.4
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + CLE +
## DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR +
## NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CLE 1 0.1 11546 -23773.2
## - TEN 1 0.1 11546 -23773.2
## - avg_rectd_plyr 1 0.1 11546 -23773.2
## - MIA 1 0.1 11546 -23773.2
## - JAC 1 0.1 11546 -23773.2
## - BUF 1 0.1 11546 -23773.2
## - MINN 1 0.1 11546 -23773.1
## - NE 1 0.1 11546 -23773.1
## - PHI 1 0.2 11546 -23773.0
## - BAL 1 0.2 11546 -23772.9
## - SD 1 0.2 11546 -23772.9
## - NYG 1 0.2 11546 -23772.9
## - CHI 1 0.2 11546 -23772.8
## - DET 1 0.3 11546 -23772.8
## - avg_rbry_pos 1 0.3 11546 -23772.8
## - STL 1 0.3 11546 -23772.8
## - IND 1 0.5 11547 -23772.2
## - HOU 1 0.6 11547 -23772.0
## - WAS 1 0.7 11547 -23771.8
## - GB 1 0.7 11547 -23771.8
## - SEA 1 0.8 11547 -23771.4
## <none> 11546 -23771.4
## - DEN 1 0.9 11547 -23771.1
## - bad_weather_1 1 1.1 11547 -23770.8
## - CAR 1 1.2 11547 -23770.6
## - PIT 1 1.2 11548 -23770.4
## - NYJ 1 1.3 11548 -23770.3
## - grass_1 1 1.4 11548 -23770.1
## - NOR 1 1.5 11548 -23769.8
## - home_team_1 1 2.3 11548 -23767.9
## - cold_weather 1 4.9 11551 -23761.8
## - avg_rbry_plyr 1 7923.9 19470 -9412.3
##
## Step: AIC=-23773.25
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN +
## DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR + NYG +
## NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - TEN 1 0.1 11546 -23775.1
## - MIA 1 0.1 11546 -23775.1
## - avg_rectd_plyr 1 0.1 11546 -23775.1
## - JAC 1 0.1 11546 -23775.0
## - BUF 1 0.1 11546 -23775.0
## - MINN 1 0.1 11546 -23775.0
## - NE 1 0.2 11546 -23774.9
## - NYG 1 0.2 11546 -23774.8
## - PHI 1 0.2 11546 -23774.7
## - BAL 1 0.2 11546 -23774.7
## - DET 1 0.2 11546 -23774.7
## - STL 1 0.2 11546 -23774.7
## - SD 1 0.2 11546 -23774.7
## - avg_rbry_pos 1 0.3 11546 -23774.6
## - CHI 1 0.3 11547 -23774.6
## - HOU 1 0.5 11547 -23774.0
## - IND 1 0.6 11547 -23773.9
## - WAS 1 0.6 11547 -23773.7
## - GB 1 0.7 11547 -23773.5
## <none> 11546 -23773.2
## - SEA 1 0.9 11547 -23773.1
## - DEN 1 0.9 11547 -23773.1
## - bad_weather_1 1 1.1 11547 -23772.6
## - CAR 1 1.3 11548 -23772.3
## - PIT 1 1.3 11548 -23772.1
## - grass_1 1 1.4 11548 -23772.0
## - NYJ 1 1.4 11548 -23771.9
## - NOR 1 1.6 11548 -23771.4
## - home_team_1 1 2.4 11549 -23769.6
## - cold_weather 1 5.0 11551 -23763.4
## - avg_rbry_plyr 1 7923.9 19470 -9414.2
##
## Step: AIC=-23775.11
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN +
## DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR + NYG +
## NYJ + PHI + PIT + SD + SEA + STL + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.1 11546 -23777.0
## - avg_rectd_plyr 1 0.1 11546 -23776.9
## - JAC 1 0.1 11546 -23776.8
## - BUF 1 0.1 11546 -23776.8
## - MINN 1 0.1 11546 -23776.8
## - NE 1 0.2 11546 -23776.7
## - NYG 1 0.2 11546 -23776.7
## - DET 1 0.2 11547 -23776.6
## - STL 1 0.2 11547 -23776.6
## - PHI 1 0.2 11547 -23776.5
## - BAL 1 0.2 11547 -23776.5
## - avg_rbry_pos 1 0.2 11547 -23776.5
## - SD 1 0.3 11547 -23776.4
## - CHI 1 0.3 11547 -23776.4
## - HOU 1 0.5 11547 -23775.9
## - IND 1 0.6 11547 -23775.7
## - WAS 1 0.6 11547 -23775.7
## - GB 1 0.8 11547 -23775.2
## <none> 11546 -23775.1
## - DEN 1 0.9 11547 -23775.1
## - SEA 1 0.9 11547 -23774.8
## - bad_weather_1 1 1.1 11547 -23774.5
## - CAR 1 1.3 11548 -23773.9
## - grass_1 1 1.3 11548 -23773.9
## - PIT 1 1.4 11548 -23773.7
## - NYJ 1 1.5 11548 -23773.6
## - NOR 1 1.7 11548 -23773.1
## - home_team_1 1 2.4 11549 -23771.4
## - cold_weather 1 5.0 11551 -23765.2
## - avg_rbry_plyr 1 7924.1 19471 -9415.9
##
## Step: AIC=-23776.97
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN +
## DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYG + NYJ +
## PHI + PIT + SD + SEA + STL + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_rectd_plyr 1 0.1 11546 -23778.8
## - JAC 1 0.1 11546 -23778.6
## - BUF 1 0.1 11546 -23778.6
## - MINN 1 0.2 11547 -23778.6
## - NYG 1 0.2 11547 -23778.6
## - NE 1 0.2 11547 -23778.5
## - DET 1 0.2 11547 -23778.5
## - STL 1 0.2 11547 -23778.5
## - avg_rbry_pos 1 0.3 11547 -23778.4
## - PHI 1 0.3 11547 -23778.3
## - BAL 1 0.3 11547 -23778.3
## - SD 1 0.3 11547 -23778.2
## - CHI 1 0.3 11547 -23778.2
## - HOU 1 0.5 11547 -23777.8
## - WAS 1 0.6 11547 -23777.6
## - IND 1 0.6 11547 -23777.5
## - DEN 1 0.8 11547 -23777.0
## <none> 11546 -23777.0
## - GB 1 0.8 11547 -23776.9
## - SEA 1 1.0 11547 -23776.6
## - bad_weather_1 1 1.1 11548 -23776.4
## - grass_1 1 1.3 11548 -23775.8
## - CAR 1 1.4 11548 -23775.6
## - PIT 1 1.5 11548 -23775.4
## - NYJ 1 1.5 11548 -23775.3
## - NOR 1 1.7 11548 -23774.8
## - home_team_1 1 2.4 11549 -23773.2
## - cold_weather 1 5.0 11551 -23767.1
## - avg_rbry_plyr 1 7925.1 19472 -9416.4
##
## Step: AIC=-23778.78
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN +
## DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYG + NYJ +
## PHI + PIT + SD + SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - JAC 1 0.1 11547 -23780.4
## - BUF 1 0.1 11547 -23780.4
## - MINN 1 0.2 11547 -23780.4
## - NYG 1 0.2 11547 -23780.4
## - NE 1 0.2 11547 -23780.4
## - avg_rbry_pos 1 0.2 11547 -23780.3
## - STL 1 0.2 11547 -23780.3
## - DET 1 0.2 11547 -23780.3
## - PHI 1 0.3 11547 -23780.2
## - BAL 1 0.3 11547 -23780.1
## - SD 1 0.3 11547 -23780.1
## - CHI 1 0.3 11547 -23780.0
## - HOU 1 0.5 11547 -23779.6
## - WAS 1 0.6 11547 -23779.4
## - IND 1 0.6 11547 -23779.3
## - GB 1 0.8 11547 -23778.9
## <none> 11546 -23778.8
## - DEN 1 0.9 11547 -23778.8
## - SEA 1 1.0 11548 -23778.4
## - bad_weather_1 1 1.1 11548 -23778.2
## - grass_1 1 1.3 11548 -23777.6
## - CAR 1 1.4 11548 -23777.5
## - PIT 1 1.5 11548 -23777.3
## - NYJ 1 1.5 11548 -23777.1
## - NOR 1 1.7 11548 -23776.7
## - home_team_1 1 2.4 11549 -23775.0
## - cold_weather 1 5.0 11551 -23769.0
## - avg_rbry_plyr 1 7948.1 19495 -9385.8
##
## Step: AIC=-23780.44
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN +
## DET + GB + HOU + IND + MINN + NE + NOR + NYG + NYJ + PHI +
## PIT + SD + SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.1 11547 -23782.1
## - MINN 1 0.1 11547 -23782.1
## - NE 1 0.2 11547 -23782.1
## - avg_rbry_pos 1 0.2 11547 -23782.0
## - NYG 1 0.2 11547 -23782.0
## - STL 1 0.2 11547 -23781.9
## - PHI 1 0.2 11547 -23781.9
## - DET 1 0.2 11547 -23781.9
## - BAL 1 0.2 11547 -23781.9
## - SD 1 0.3 11547 -23781.8
## - CHI 1 0.3 11547 -23781.7
## - HOU 1 0.5 11547 -23781.2
## - IND 1 0.6 11547 -23781.1
## - WAS 1 0.6 11547 -23780.9
## - GB 1 0.8 11547 -23780.6
## <none> 11547 -23780.4
## - DEN 1 0.9 11548 -23780.2
## - SEA 1 0.9 11548 -23780.2
## - bad_weather_1 1 1.1 11548 -23779.9
## - CAR 1 1.3 11548 -23779.3
## - grass_1 1 1.4 11548 -23779.2
## - PIT 1 1.4 11548 -23779.1
## - NYJ 1 1.5 11548 -23778.9
## - NOR 1 1.6 11548 -23778.6
## - home_team_1 1 2.4 11549 -23776.8
## - cold_weather 1 5.0 11552 -23770.5
## - avg_rbry_plyr 1 7948.4 19495 -9387.3
##
## Step: AIC=-23782.13
## ry ~ cold_weather + home_team_1 + BAL + CAR + CHI + DEN + DET +
## GB + HOU + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT +
## SD + SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MINN 1 0.1 11547 -23783.8
## - NE 1 0.1 11547 -23783.8
## - avg_rbry_pos 1 0.2 11547 -23783.7
## - PHI 1 0.2 11547 -23783.6
## - BAL 1 0.2 11547 -23783.6
## - NYG 1 0.2 11547 -23783.6
## - SD 1 0.2 11547 -23783.6
## - STL 1 0.2 11547 -23783.5
## - DET 1 0.3 11547 -23783.5
## - CHI 1 0.3 11547 -23783.5
## - IND 1 0.5 11547 -23782.8
## - HOU 1 0.6 11547 -23782.8
## - WAS 1 0.7 11547 -23782.5
## - GB 1 0.7 11548 -23782.4
## <none> 11547 -23782.1
## - SEA 1 0.9 11548 -23782.0
## - DEN 1 1.0 11548 -23781.8
## - bad_weather_1 1 1.1 11548 -23781.6
## - grass_1 1 1.3 11548 -23781.1
## - CAR 1 1.3 11548 -23781.1
## - PIT 1 1.3 11548 -23780.9
## - NYJ 1 1.4 11548 -23780.8
## - NOR 1 1.6 11548 -23780.4
## - home_team_1 1 2.3 11549 -23778.6
## - cold_weather 1 5.0 11552 -23772.3
## - avg_rbry_plyr 1 7949.1 19496 -9388.1
##
## Step: AIC=-23783.84
## ry ~ cold_weather + home_team_1 + BAL + CAR + CHI + DEN + DET +
## GB + HOU + IND + NE + NOR + NYG + NYJ + PHI + PIT + SD +
## SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NE 1 0.1 11547 -23785.6
## - BAL 1 0.2 11547 -23785.4
## - PHI 1 0.2 11547 -23785.4
## - avg_rbry_pos 1 0.2 11547 -23785.4
## - SD 1 0.2 11547 -23785.3
## - NYG 1 0.3 11547 -23785.2
## - CHI 1 0.3 11547 -23785.2
## - STL 1 0.3 11547 -23785.2
## - DET 1 0.3 11547 -23785.1
## - IND 1 0.5 11547 -23784.6
## - HOU 1 0.6 11548 -23784.4
## - GB 1 0.7 11548 -23784.2
## - WAS 1 0.7 11548 -23784.1
## - SEA 1 0.8 11548 -23783.9
## <none> 11547 -23783.8
## - DEN 1 1.0 11548 -23783.4
## - bad_weather_1 1 1.1 11548 -23783.3
## - grass_1 1 1.2 11548 -23782.9
## - CAR 1 1.2 11548 -23782.9
## - PIT 1 1.3 11548 -23782.7
## - NYJ 1 1.3 11548 -23782.6
## - NOR 1 1.5 11548 -23782.3
## - home_team_1 1 2.3 11549 -23780.3
## - cold_weather 1 4.9 11552 -23774.1
## - avg_rbry_plyr 1 7955.5 19502 -9380.9
##
## Step: AIC=-23785.59
## ry ~ cold_weather + home_team_1 + BAL + CAR + CHI + DEN + DET +
## GB + HOU + IND + NOR + NYG + NYJ + PHI + PIT + SD + SEA +
## STL + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BAL 1 0.2 11547 -23787
## - PHI 1 0.2 11547 -23787
## - avg_rbry_pos 1 0.2 11547 -23787
## - SD 1 0.2 11547 -23787
## - CHI 1 0.2 11547 -23787
## - NYG 1 0.3 11547 -23787
## - STL 1 0.3 11547 -23787
## - DET 1 0.3 11547 -23787
## - IND 1 0.5 11547 -23787
## - GB 1 0.6 11548 -23786
## - HOU 1 0.6 11548 -23786
## - WAS 1 0.8 11548 -23786
## - SEA 1 0.8 11548 -23786
## <none> 11547 -23786
## - bad_weather_1 1 1.1 11548 -23785
## - DEN 1 1.1 11548 -23785
## - grass_1 1 1.1 11548 -23785
## - CAR 1 1.2 11548 -23785
## - PIT 1 1.3 11548 -23785
## - NYJ 1 1.3 11548 -23785
## - NOR 1 1.4 11548 -23784
## - home_team_1 1 2.3 11549 -23782
## - cold_weather 1 4.8 11552 -23776
## - avg_rbry_plyr 1 7956.1 19503 -9382
##
## Step: AIC=-23787.19
## ry ~ cold_weather + home_team_1 + CAR + CHI + DEN + DET + GB +
## HOU + IND + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL +
## WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PHI 1 0.2 11547 -23788.8
## - SD 1 0.2 11547 -23788.8
## - avg_rbry_pos 1 0.2 11547 -23788.7
## - CHI 1 0.2 11547 -23788.7
## - NYG 1 0.3 11548 -23788.4
## - STL 1 0.3 11548 -23788.4
## - DET 1 0.4 11548 -23788.3
## - IND 1 0.4 11548 -23788.1
## - GB 1 0.6 11548 -23787.8
## - HOU 1 0.7 11548 -23787.5
## - SEA 1 0.7 11548 -23787.4
## - WAS 1 0.8 11548 -23787.3
## <none> 11547 -23787.2
## - bad_weather_1 1 1.1 11548 -23786.6
## - grass_1 1 1.1 11548 -23786.6
## - DEN 1 1.1 11548 -23786.5
## - CAR 1 1.1 11548 -23786.5
## - PIT 1 1.2 11548 -23786.3
## - NYJ 1 1.2 11548 -23786.3
## - NOR 1 1.4 11548 -23785.9
## - home_team_1 1 2.2 11549 -23783.9
## - cold_weather 1 4.8 11552 -23777.9
## - avg_rbry_plyr 1 7959.8 19507 -9378.4
##
## Step: AIC=-23788.83
## ry ~ cold_weather + home_team_1 + CAR + CHI + DEN + DET + GB +
## HOU + IND + NOR + NYG + NYJ + PIT + SD + SEA + STL + WAS +
## avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SD 1 0.2 11548 -23790.4
## - CHI 1 0.2 11548 -23790.4
## - avg_rbry_pos 1 0.2 11548 -23790.4
## - NYG 1 0.4 11548 -23790.0
## - STL 1 0.4 11548 -23790.0
## - DET 1 0.4 11548 -23789.9
## - IND 1 0.4 11548 -23789.8
## - GB 1 0.6 11548 -23789.5
## - SEA 1 0.7 11548 -23789.2
## - HOU 1 0.7 11548 -23789.1
## <none> 11547 -23788.8
## - WAS 1 0.9 11548 -23788.8
## - bad_weather_1 1 1.1 11548 -23788.3
## - CAR 1 1.1 11548 -23788.2
## - PIT 1 1.1 11548 -23788.1
## - grass_1 1 1.2 11548 -23788.1
## - NYJ 1 1.2 11548 -23788.0
## - DEN 1 1.2 11548 -23788.0
## - NOR 1 1.3 11549 -23787.6
## - home_team_1 1 2.2 11550 -23785.6
## - cold_weather 1 4.7 11552 -23779.6
## - avg_rbry_plyr 1 7966.8 19514 -9370.4
##
## Step: AIC=-23790.43
## ry ~ cold_weather + home_team_1 + CAR + CHI + DEN + DET + GB +
## HOU + IND + NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr +
## avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CHI 1 0.2 11548 -23792.0
## - avg_rbry_pos 1 0.2 11548 -23792.0
## - NYG 1 0.4 11548 -23791.5
## - STL 1 0.4 11548 -23791.5
## - IND 1 0.4 11548 -23791.5
## - DET 1 0.4 11548 -23791.5
## - GB 1 0.5 11548 -23791.2
## - SEA 1 0.7 11548 -23790.8
## - HOU 1 0.8 11548 -23790.6
## <none> 11548 -23790.4
## - WAS 1 0.9 11548 -23790.3
## - CAR 1 1.0 11548 -23789.9
## - bad_weather_1 1 1.1 11549 -23789.8
## - PIT 1 1.1 11549 -23789.8
## - NYJ 1 1.2 11549 -23789.7
## - DEN 1 1.3 11549 -23789.4
## - grass_1 1 1.3 11549 -23789.4
## - NOR 1 1.3 11549 -23789.3
## - home_team_1 1 2.2 11550 -23787.3
## - cold_weather 1 4.8 11552 -23781.0
## - avg_rbry_plyr 1 7970.7 19518 -9366.6
##
## Step: AIC=-23792.02
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU +
## IND + NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr +
## avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_rbry_pos 1 0.2 11548 -23793.5
## - IND 1 0.4 11548 -23793.1
## - NYG 1 0.4 11548 -23793.1
## - STL 1 0.4 11548 -23793.1
## - DET 1 0.4 11548 -23793.0
## - GB 1 0.5 11548 -23792.8
## - SEA 1 0.6 11548 -23792.5
## - HOU 1 0.8 11548 -23792.1
## <none> 11548 -23792.0
## - WAS 1 1.0 11549 -23791.7
## - CAR 1 1.0 11549 -23791.6
## - PIT 1 1.0 11549 -23791.5
## - bad_weather_1 1 1.1 11549 -23791.5
## - NYJ 1 1.1 11549 -23791.4
## - NOR 1 1.3 11549 -23791.0
## - DEN 1 1.3 11549 -23790.9
## - grass_1 1 1.3 11549 -23790.9
## - home_team_1 1 2.2 11550 -23788.9
## - cold_weather 1 4.7 11552 -23782.7
## - avg_rbry_plyr 1 7973.7 19521 -9364.2
##
## Step: AIC=-23793.55
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU +
## IND + NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - IND 1 0.4 11548 -23794.6
## - STL 1 0.4 11548 -23794.6
## - NYG 1 0.4 11548 -23794.6
## - DET 1 0.4 11548 -23794.5
## - GB 1 0.5 11548 -23794.4
## - SEA 1 0.7 11548 -23794.0
## - HOU 1 0.8 11549 -23793.7
## <none> 11548 -23793.5
## - WAS 1 1.0 11549 -23793.3
## - CAR 1 1.0 11549 -23793.1
## - PIT 1 1.1 11549 -23793.0
## - bad_weather_1 1 1.1 11549 -23793.0
## - NYJ 1 1.1 11549 -23792.9
## - NOR 1 1.2 11549 -23792.6
## - DEN 1 1.3 11549 -23792.4
## - grass_1 1 1.3 11549 -23792.4
## - home_team_1 1 2.2 11550 -23790.4
## - cold_weather 1 4.7 11553 -23784.3
## - avg_rbry_plyr 1 15898.1 27446 -2.1
##
## Step: AIC=-23794.64
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU +
## NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - NYG 1 0.5 11549 -23795.6
## - STL 1 0.5 11549 -23795.6
## - GB 1 0.5 11549 -23795.5
## - DET 1 0.5 11549 -23795.5
## - SEA 1 0.6 11549 -23795.2
## <none> 11548 -23794.6
## - HOU 1 0.9 11549 -23794.6
## - CAR 1 1.0 11549 -23794.3
## - WAS 1 1.0 11549 -23794.3
## - PIT 1 1.0 11549 -23794.2
## - NYJ 1 1.1 11549 -23794.1
## - bad_weather_1 1 1.1 11549 -23794.1
## - NOR 1 1.1 11549 -23793.9
## - grass_1 1 1.2 11549 -23793.8
## - DEN 1 1.4 11550 -23793.4
## - home_team_1 1 2.3 11551 -23791.1
## - cold_weather 1 4.8 11553 -23785.3
## - avg_rbry_plyr 1 15899.7 27448 -2.1
##
## Step: AIC=-23795.56
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU +
## NOR + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - STL 1 0.4 11549 -23796.6
## - DET 1 0.5 11549 -23796.5
## - GB 1 0.5 11549 -23796.3
## - SEA 1 0.7 11549 -23796.0
## - HOU 1 0.8 11550 -23795.6
## <none> 11549 -23795.6
## - WAS 1 0.9 11550 -23795.3
## - CAR 1 1.0 11550 -23795.1
## - PIT 1 1.1 11550 -23795.0
## - bad_weather_1 1 1.1 11550 -23794.9
## - NYJ 1 1.1 11550 -23794.8
## - NOR 1 1.2 11550 -23794.6
## - DEN 1 1.3 11550 -23794.5
## - grass_1 1 1.4 11550 -23794.3
## - home_team_1 1 2.4 11551 -23791.8
## - cold_weather 1 4.9 11554 -23785.9
## - avg_rbry_plyr 1 15899.7 27448 -3.7
##
## Step: AIC=-23796.57
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU +
## NOR + NYJ + PIT + SEA + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DET 1 0.4 11550 -23797.6
## - GB 1 0.5 11550 -23797.3
## - SEA 1 0.7 11550 -23796.8
## - HOU 1 0.7 11550 -23796.8
## <none> 11549 -23796.6
## - WAS 1 0.9 11550 -23796.4
## - CAR 1 1.1 11550 -23796.0
## - bad_weather_1 1 1.1 11550 -23796.0
## - PIT 1 1.1 11550 -23795.9
## - NYJ 1 1.2 11550 -23795.7
## - DEN 1 1.3 11550 -23795.6
## - NOR 1 1.3 11550 -23795.4
## - grass_1 1 1.5 11551 -23795.1
## - home_team_1 1 2.3 11551 -23793.2
## - cold_weather 1 4.8 11554 -23787.0
## - avg_rbry_plyr 1 15901.8 27451 -3.1
##
## Step: AIC=-23797.61
## ry ~ cold_weather + home_team_1 + CAR + DEN + GB + HOU + NOR +
## NYJ + PIT + SEA + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - GB 1 0.6 11550 -23798
## - HOU 1 0.7 11550 -23798
## - SEA 1 0.8 11550 -23798
## <none> 11550 -23798
## - WAS 1 0.9 11550 -23798
## - bad_weather_1 1 1.1 11551 -23797
## - CAR 1 1.1 11551 -23797
## - PIT 1 1.2 11551 -23797
## - DEN 1 1.2 11551 -23797
## - NYJ 1 1.3 11551 -23797
## - NOR 1 1.4 11551 -23796
## - grass_1 1 1.6 11551 -23796
## - home_team_1 1 2.2 11552 -23795
## - cold_weather 1 4.7 11554 -23788
## - avg_rbry_plyr 1 15902.5 27452 -4
##
## Step: AIC=-23798.23
## ry ~ cold_weather + home_team_1 + CAR + DEN + HOU + NOR + NYJ +
## PIT + SEA + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.7 11551 -23798.5
## - HOU 1 0.7 11551 -23798.5
## <none> 11550 -23798.2
## - WAS 1 0.9 11551 -23798.0
## - CAR 1 1.1 11551 -23797.7
## - bad_weather_1 1 1.1 11551 -23797.7
## - PIT 1 1.1 11551 -23797.7
## - NYJ 1 1.2 11551 -23797.3
## - DEN 1 1.3 11551 -23797.1
## - NOR 1 1.4 11551 -23797.0
## - grass_1 1 1.7 11552 -23796.1
## - home_team_1 1 2.1 11552 -23795.2
## - cold_weather 1 4.5 11555 -23789.5
## - avg_rbry_plyr 1 15902.0 27452 -5.9
##
## Step: AIC=-23798.52
## ry ~ cold_weather + home_team_1 + CAR + DEN + HOU + NOR + NYJ +
## PIT + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - HOU 1 0.8 11552 -23798.6
## <none> 11551 -23798.5
## - CAR 1 1.0 11552 -23798.1
## - PIT 1 1.0 11552 -23798.1
## - WAS 1 1.0 11552 -23798.1
## - bad_weather_1 1 1.0 11552 -23798.0
## - NYJ 1 1.1 11552 -23797.9
## - NOR 1 1.3 11552 -23797.5
## - DEN 1 1.4 11552 -23797.2
## - grass_1 1 1.5 11552 -23796.9
## - home_team_1 1 2.0 11553 -23795.8
## - cold_weather 1 4.3 11555 -23790.3
## - avg_rbry_plyr 1 15903.5 27454 -5.7
##
## Step: AIC=-23798.65
## ry ~ cold_weather + home_team_1 + CAR + DEN + NOR + NYJ + PIT +
## WAS + avg_rbry_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## <none> 11552 -23799
## - WAS 1 1.0 11552 -23798
## - PIT 1 1.0 11553 -23798
## - CAR 1 1.1 11553 -23798
## - bad_weather_1 1 1.1 11553 -23798
## - NYJ 1 1.2 11553 -23798
## - DEN 1 1.3 11553 -23798
## - NOR 1 1.4 11553 -23797
## - grass_1 1 1.6 11553 -23797
## - home_team_1 1 1.8 11553 -23797
## - cold_weather 1 4.2 11556 -23791
## - avg_rbry_plyr 1 15904.5 27456 -6Rushing attempts
PreProcess:
set.seed(123)
splitra <- sample.split(nfl_data$ra, SplitRatio = 0.7)
Trainra <- subset(nfl_data, split == TRUE)
Testra <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainra, method = c("center", "scale"))
trainTransformedra <- predict(preProcValues, Trainra)
testTransformedra <- predict(preProcValues, Testra)ggpairs:
ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[46:51]))])
raregform <- formula(paste("ra ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegRushAtt <- lm(raregform, data = trainTransformedra)
summary(linRegRushAtt)##
## Call:
## lm(formula = raregform, data = trainTransformedra)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8046 -0.0854 -0.0090 0.0496 5.3831
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.104e-15 3.326e-03 0.000 1.000000
## height -2.162e-03 6.453e-03 -0.335 0.737573
## weight -1.279e-03 6.048e-03 -0.212 0.832493
## cold_weather 1.184e-02 3.501e-03 3.381 0.000724 ***
## hot_weather -3.506e-03 3.356e-03 -1.045 0.296176
## home_team_1 5.312e-03 3.619e-03 1.468 0.142168
## forty1 2.705e-02 5.740e-03 4.712 2.46e-06 ***
## vertical1 2.959e-04 4.413e-03 0.067 0.946539
## ARI 7.646e-03 4.653e-03 1.643 0.100312
## ATL 6.424e-03 4.675e-03 1.374 0.169437
## BAL 7.016e-03 4.679e-03 1.499 0.133760
## BUF -8.683e-04 4.619e-03 -0.188 0.850888
## CAR -2.889e-03 4.589e-03 -0.630 0.528932
## CHI 2.194e-03 4.537e-03 0.483 0.628766
## CIN 9.587e-03 4.621e-03 2.075 0.038017 *
## CLE 9.419e-03 4.600e-03 2.048 0.040589 *
## DAL 2.418e-03 4.646e-03 0.521 0.602708
## DEN 1.599e-02 4.664e-03 3.429 0.000607 ***
## DET 1.059e-02 4.600e-03 2.302 0.021340 *
## GB 5.605e-04 4.735e-03 0.118 0.905783
## HOU 1.138e-02 4.679e-03 2.432 0.015023 *
## IND 2.856e-03 4.645e-03 0.615 0.538603
## JAC 2.146e-03 4.531e-03 0.474 0.635752
## KC -3.085e-03 4.630e-03 -0.666 0.505194
## MIA 3.608e-03 4.556e-03 0.792 0.428412
## MINN -6.259e-03 4.584e-03 -1.365 0.172130
## NE 6.544e-03 4.787e-03 1.367 0.171597
## NOR -1.954e-03 4.772e-03 -0.409 0.682181
## NYG 1.218e-02 4.665e-03 2.611 0.009035 **
## NYJ -2.709e-03 4.647e-03 -0.583 0.560015
## OAK 2.270e-03 4.677e-03 0.485 0.627353
## PHI -4.940e-03 4.532e-03 -1.090 0.275639
## PIT 1.039e-03 4.651e-03 0.223 0.823167
## SD 8.241e-03 4.564e-03 1.806 0.070952 .
## SEA -2.708e-03 4.736e-03 -0.572 0.567490
## STL 1.129e-02 4.610e-03 2.449 0.014334 *
## TB 5.189e-03 4.567e-03 1.136 0.255896
## TEN 6.032e-03 4.594e-03 1.313 0.189196
## WAS 7.307e-03 4.619e-03 1.582 0.113631
## avg_trg_team NA NA NA NA
## avg_rectd_plyr -1.540e-03 4.247e-03 -0.363 0.716951
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr 7.971e-01 5.083e-03 156.823 < 2e-16 ***
## avg_rbry_pos 5.532e-02 5.922e-03 9.341 < 2e-16 ***
## avg_fuml_plyr 1.334e-03 4.913e-03 0.271 0.786013
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -3.404e-03 5.337e-03 -0.638 0.523639
## avg_qbtdp_team NA NA NA NA
## grass_1 -3.779e-03 3.827e-03 -0.987 0.323445
## bad_weather_1 2.234e-03 3.383e-03 0.660 0.509067
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5514 on 27438 degrees of freedom
## Multiple R-squared: 0.6965, Adjusted R-squared: 0.696
## F-statistic: 1399 on 45 and 27438 DF, p-value: < 2.2e-16linRegRushAtt2 <- update(linRegRushYd,~.-height-weight-hot_weather-home_team_1-age-is_TE
-vertical1-ARI-ATL-BAL - BUF - CAR - CHI
-CIN - CLE - DAL - GB - IND - JAC - KC - MIA
-MINN - NE - NOR -NYJ - OAK - PHI - PIT -SD - SEA
-TB - TEN - WAS
-avg_rectd_plyr-avg_trg_team-avg_tdr_team-avg_rbra_team
-avg_fuml_team-avg_fuml_plyr-avg_qbints_team-avg_qbtdp_team-avg_qbints_plyr
-bad_weather_1-grass_1)
summary(linRegRushAtt2)##
## Call:
## lm(formula = ry ~ cold_weather + forty1 + DEN + DET + HOU + NYG +
## STL + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr, data = trainTransformedry)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4811 -0.0751 -0.0163 0.0151 7.1750
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.336e-14 3.912e-03 0.000 1.000000
## cold_weather 1.442e-02 3.938e-03 3.662 0.000251 ***
## forty1 -1.982e-04 4.525e-03 -0.044 0.965059
## DEN 7.910e-03 3.924e-03 2.016 0.043855 *
## DET 4.997e-03 3.933e-03 1.271 0.203905
## HOU 6.066e-03 3.935e-03 1.541 0.123208
## NYG 6.172e-03 3.929e-03 1.571 0.116167
## STL 4.426e-03 3.928e-03 1.127 0.259865
## avg_rbry_plyr 7.584e-01 5.588e-03 135.723 < 2e-16 ***
## avg_rbry_pos 4.004e-03 5.521e-03 0.725 0.468327
## avg_qbtdp_plyr -1.094e-03 4.459e-03 -0.245 0.806247
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6486 on 27473 degrees of freedom
## Multiple R-squared: 0.5795, Adjusted R-squared: 0.5793
## F-statistic: 3786 on 10 and 27473 DF, p-value: < 2.2e-16linRegRushAtt3 <- update(linRegRushYd,~.-is_WR-forty1-is_TE-DET-HOU-NYG-STL-avg_rbry_pos)
summary(linRegRushAtt3)##
## Call:
## lm(formula = ry ~ height + weight + cold_weather + hot_weather +
## home_team_1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + GB + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + TB + TEN +
## WAS + avg_trg_team + avg_rectd_plyr + avg_tdr_team + avg_rbra_team +
## avg_rbry_plyr + avg_fuml_plyr + avg_fuml_team + avg_qbints_team +
## avg_qbtdp_plyr + avg_qbtdp_team + grass_1 + bad_weather_1,
## data = trainTransformedry)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4896 -0.0836 -0.0125 0.0242 7.1660
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.344e-14 3.913e-03 0.000 1.000000
## height -4.250e-03 6.636e-03 -0.641 0.521852
## weight 2.594e-03 5.973e-03 0.434 0.664046
## cold_weather 1.399e-02 4.119e-03 3.396 0.000685 ***
## hot_weather -1.398e-03 3.948e-03 -0.354 0.723326
## home_team_1 1.004e-02 4.257e-03 2.357 0.018410 *
## vertical1 -1.282e-03 4.435e-03 -0.289 0.772558
## ARI 1.483e-03 1.001e-02 0.148 0.882240
## ATL 1.719e-03 1.975e-02 0.087 0.930629
## BAL -4.354e-03 1.319e-02 -0.330 0.741352
## BUF -3.768e-03 9.869e-03 -0.382 0.702625
## CAR -5.674e-03 7.359e-03 -0.771 0.440718
## CHI -8.120e-03 9.801e-03 -0.828 0.407412
## CIN -4.125e-03 7.453e-03 -0.553 0.579998
## CLE -1.419e-03 5.366e-03 -0.265 0.791380
## DAL -1.644e-03 5.768e-03 -0.285 0.775585
## DEN 1.147e-04 2.093e-02 0.005 0.995629
## GB -6.551e-03 8.796e-03 -0.745 0.456438
## IND -9.439e-03 4.924e-03 -1.917 0.055243 .
## JAC -8.556e-03 8.212e-03 -1.042 0.297482
## KC -6.296e-04 5.422e-03 -0.116 0.907560
## MIA -1.145e-03 5.612e-03 -0.204 0.838315
## MINN 1.818e-03 1.202e-02 0.151 0.879798
## NE 3.165e-03 3.194e-02 0.099 0.921068
## NOR -4.459e-03 2.444e-02 -0.182 0.855199
## NYJ -1.296e-02 1.418e-02 -0.914 0.360618
## OAK 1.173e-03 1.366e-02 0.086 0.931562
## PHI -4.167e-03 1.563e-02 -0.267 0.789842
## PIT -9.834e-03 5.091e-03 -1.932 0.053398 .
## SD -1.064e-02 1.536e-02 -0.693 0.488426
## SEA -3.444e-03 1.131e-02 -0.305 0.760741
## TB -5.047e-03 1.117e-02 -0.452 0.651391
## TEN 1.429e-03 6.043e-03 0.236 0.813091
## WAS 6.074e-03 6.196e-03 0.980 0.326982
## avg_trg_team 7.333e-03 8.678e-03 0.845 0.398129
## avg_rectd_plyr 1.483e-03 4.720e-03 0.314 0.753296
## avg_tdr_team -2.054e-02 3.991e-02 -0.515 0.606745
## avg_rbra_team 1.626e-02 4.065e-02 0.400 0.689110
## avg_rbry_plyr 7.604e-01 4.902e-03 155.133 < 2e-16 ***
## avg_fuml_plyr 7.528e-04 5.779e-03 0.130 0.896352
## avg_fuml_team 4.848e-03 4.544e-02 0.107 0.915024
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -3.021e-04 6.019e-03 -0.050 0.959977
## avg_qbtdp_team NA NA NA NA
## grass_1 -7.836e-03 4.502e-03 -1.741 0.081769 .
## bad_weather_1 6.398e-03 3.980e-03 1.607 0.107989
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6487 on 27440 degrees of freedom
## Multiple R-squared: 0.5799, Adjusted R-squared: 0.5792
## F-statistic: 880.8 on 43 and 27440 DF, p-value: < 2.2e-16Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
RushattPredicted <- predict(linRegRushAtt, newdata = testTransformedra)## Warning in predict.lm(linRegRushAtt, newdata = testTransformedra):
## prediction from a rank-deficient fit may be misleadingSSEruatt <- sum((RushattPredicted - testTransformedra$ra)^2)
SSTruatt <- sum((mean(nfl_data$ra)-testTransformedra$ra)^2)
r2_ruatt <- 1 - SSEruatt/SSTruatt
r2_ruatt## [1] 0.958404rmse_ruatt <- sqrt(SSEruatt/nrow(testTransformedra))
rmse_ruatt## [1] 0.5583721Regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegRushAtt3, which = c(1:3,2))
Summary statistics:
confint(linRegRushAtt3)## 2.5 % 97.5 %
## (Intercept) -0.007669245 0.0076692451
## height -0.017256818 0.0087562940
## weight -0.009113117 0.0143017475
## cold_weather 0.005913936 0.0220595475
## hot_weather -0.009137059 0.0063413757
## home_team_1 0.001691644 0.0183806622
## vertical1 -0.009974415 0.0074107595
## ARI -0.018134356 0.0210994601
## ATL -0.036992629 0.0404313835
## BAL -0.030210343 0.0215021045
## BUF -0.023112326 0.0155764292
## CAR -0.020098113 0.0087504440
## CHI -0.027330666 0.0110907770
## CIN -0.018733519 0.0104842673
## CLE -0.011937414 0.0090984867
## DAL -0.012949042 0.0096605859
## DEN -0.040914291 0.0411436294
## GB -0.023792568 0.0106904874
## IND -0.019089129 0.0002117549
## JAC -0.024651979 0.0075401749
## KC -0.011257522 0.0099982754
## MIA -0.012145205 0.0098548783
## MINN -0.021742134 0.0253776222
## NE -0.059432674 0.0657618248
## NOR -0.052353695 0.0434352291
## NYJ -0.040754676 0.0148292770
## OAK -0.025602975 0.0279494003
## PHI -0.034808261 0.0264752052
## PIT -0.019811999 0.0001439443
## SD -0.040745213 0.0194631912
## SEA -0.025611367 0.0187235469
## TB -0.026939122 0.0168457355
## TEN -0.010416503 0.0132743474
## WAS -0.006071133 0.0182184220
## avg_trg_team -0.009676353 0.0243414921
## avg_rectd_plyr -0.007767648 0.0107345278
## avg_tdr_team -0.098773936 0.0576858279
## avg_rbra_team -0.063405957 0.0959277180
## avg_rbry_plyr 0.750805188 0.7700203321
## avg_fuml_plyr -0.010573740 0.0120793526
## avg_fuml_team -0.084210860 0.0939076059
## avg_qbints_team NA NA
## avg_qbtdp_plyr -0.012100583 0.0114964322
## avg_qbtdp_team NA NA
## grass_1 -0.016659292 0.0009880277
## bad_weather_1 -0.001403838 0.0141992619coef(summary(linRegRushAtt3))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.344479e-14 0.003912779 5.991850e-12 1.0000000000
## height -4.250262e-03 0.006635827 -6.405022e-01 0.5218515088
## weight 2.594315e-03 0.005973026 4.343385e-01 0.6640460685
## cold_weather 1.398674e-02 0.004118672 3.395935e+00 0.0006849163
## hot_weather -1.397841e-03 0.003948479 -3.540203e-01 0.7233264149
## home_team_1 1.003615e-02 0.004257293 2.357403e+00 0.0184102659
## vertical1 -1.281828e-03 0.004434879 -2.890333e-01 0.7725580582
## ARI 1.482552e-03 0.010008369 1.481312e-01 0.8822402932
## ATL 1.719377e-03 0.019750515 8.705481e-02 0.9306285825
## BAL -4.354119e-03 0.013191611 -3.300673e-01 0.7413516436
## BUF -3.767948e-03 0.009869326 -3.817837e-01 0.7026247322
## CAR -5.673834e-03 0.007359136 -7.709919e-01 0.4407183832
## CHI -8.119944e-03 0.009801136 -8.284697e-01 0.4074117522
## CIN -4.124626e-03 0.007453325 -5.533941e-01 0.5799981114
## CLE -1.419464e-03 0.005366163 -2.645211e-01 0.7913803617
## DAL -1.644228e-03 0.005767614 -2.850794e-01 0.7755854311
## DEN 1.146694e-04 0.020932604 5.478027e-03 0.9956292289
## GB -6.551040e-03 0.008796471 -7.447350e-01 0.4564383012
## IND -9.438687e-03 0.004923568 -1.917042e+00 0.0552429659
## JAC -8.555902e-03 0.008212073 -1.041869e+00 0.2974817178
## KC -6.296235e-04 0.005422258 -1.161183e-01 0.9075596145
## MIA -1.145164e-03 0.005612122 -2.040518e-01 0.8383145395
## MINN 1.817744e-03 0.012020037 1.512262e-01 0.8797984050
## NE 3.164575e-03 0.031936550 9.908945e-02 0.9210679708
## NOR -4.459233e-03 0.024435321 -1.824913e-01 0.8551985469
## NYJ -1.296270e-02 0.014179215 -9.142043e-01 0.3606175306
## OAK 1.173213e-03 0.013660969 8.588063e-02 0.9315619327
## PHI -4.166528e-03 0.015633135 -2.665190e-01 0.7898415213
## PIT -9.834027e-03 0.005090671 -1.931774e+00 0.0533976464
## SD -1.064101e-02 0.015358891 -6.928241e-01 0.4884257835
## SEA -3.443910e-03 0.011309636 -3.045111e-01 0.7607408121
## TB -5.046693e-03 0.011169319 -4.518354e-01 0.6513911628
## TEN 1.428922e-03 0.006043429 2.364423e-01 0.8130912061
## WAS 6.073644e-03 0.006196156 9.802279e-01 0.3269822992
## avg_trg_team 7.332570e-03 0.008677798 8.449804e-01 0.3981291504
## avg_rectd_plyr 1.483440e-03 0.004719821 3.143000e-01 0.7532955779
## avg_tdr_team -2.054405e-02 0.039912178 -5.147315e-01 0.6067448256
## avg_rbra_team 1.626088e-02 0.040645300 4.000679e-01 0.6891096097
## avg_rbry_plyr 7.604128e-01 0.004901696 1.551326e+02 0.0000000000
## avg_fuml_plyr 7.528063e-04 0.005778701 1.302726e-01 0.8963517388
## avg_fuml_team 4.848373e-03 0.045437215 1.067049e-01 0.9150238822
## avg_qbtdp_plyr -3.020756e-04 0.006019492 -5.018291e-02 0.9599769975
## grass_1 -7.835632e-03 0.004501752 -1.740574e+00 0.0817694614
## bad_weather_1 6.397712e-03 0.003980280 1.607352e+00 0.1079886565anova(linRegRushAtt3)## Analysis of Variance Table
##
## Response: ry
## Df Sum Sq Mean Sq F value Pr(>F)
## height 1 1821.4 1821.4 4328.6020 < 2.2e-16 ***
## weight 1 1093.9 1093.9 2599.6901 < 2.2e-16 ***
## cold_weather 1 4.0 4.0 9.5199 0.0020345 **
## hot_weather 1 0.3 0.3 0.6398 0.4238057
## home_team_1 1 3.1 3.1 7.4732 0.0062663 **
## vertical1 1 21.9 21.9 52.1045 5.399e-13 ***
## ARI 1 1.0 1.0 2.3860 0.1224362
## ATL 1 5.3 5.3 12.6629 0.0003736 ***
## BAL 1 5.7 5.7 13.5172 0.0002368 ***
## BUF 1 7.3 7.3 17.2903 3.218e-05 ***
## CAR 1 0.1 0.1 0.2082 0.6481658
## CHI 1 9.0 9.0 21.4681 3.614e-06 ***
## CIN 1 3.6 3.6 8.4879 0.0035780 **
## CLE 1 1.9 1.9 4.4084 0.0357708 *
## DAL 1 3.7 3.7 8.8898 0.0028702 **
## DEN 1 0.1 0.1 0.1739 0.6766667
## GB 1 0.7 0.7 1.7186 0.1898847
## IND 1 4.6 4.6 10.8507 0.0009888 ***
## JAC 1 2.7 2.7 6.4831 0.0108958 *
## KC 1 1.5 1.5 3.5452 0.0597286 .
## MIA 1 0.6 0.6 1.4867 0.2227429
## MINN 1 17.0 17.0 40.3101 2.201e-10 ***
## NE 1 3.0 3.0 7.2446 0.0071156 **
## NOR 1 6.0 6.0 14.3043 0.0001558 ***
## NYJ 1 2.5 2.5 5.9654 0.0145955 *
## OAK 1 1.6 1.6 3.7620 0.0524391 .
## PHI 1 3.0 3.0 7.0162 0.0080823 **
## PIT 1 0.0 0.0 0.0095 0.9222679
## SD 1 0.0 0.0 0.1015 0.7500854
## SEA 1 0.2 0.2 0.4016 0.5262656
## TB 1 0.1 0.1 0.2326 0.6296331
## TEN 1 0.0 0.0 0.0004 0.9842026
## WAS 1 5.7 5.7 13.6255 0.0002236 ***
## avg_trg_team 1 0.6 0.6 1.4230 0.2329197
## avg_rectd_plyr 1 590.5 590.5 1403.2578 < 2.2e-16 ***
## avg_tdr_team 1 8.7 8.7 20.5736 5.762e-06 ***
## avg_rbra_team 1 0.6 0.6 1.4897 0.2222670
## avg_rbry_plyr 1 12302.7 12302.7 29238.2353 < 2.2e-16 ***
## avg_fuml_plyr 1 0.0 0.0 0.0148 0.9032697
## avg_fuml_team 1 0.0 0.0 0.0524 0.8188814
## avg_qbtdp_plyr 1 0.0 0.0 0.0037 0.9517883
## grass_1 1 1.2 1.2 2.8654 0.0905158 .
## bad_weather_1 1 1.1 1.1 2.5836 0.1079887
## Residuals 27440 11546.1 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC
aic_ra <- step(lm(raregform, data = trainTransformedra), direction = "backward")## Start: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 0.0 8342.3 -32678
## - GB 1 0.0 8342.3 -32678
## - BUF 1 0.0 8342.3 -32678
## - weight 1 0.0 8342.3 -32678
## - PIT 1 0.0 8342.3 -32678
## - avg_fuml_plyr 1 0.0 8342.3 -32678
## - height 1 0.0 8342.3 -32678
## - avg_rectd_plyr 1 0.0 8342.3 -32678
## - NOR 1 0.1 8342.4 -32678
## - JAC 1 0.1 8342.4 -32678
## - CHI 1 0.1 8342.4 -32678
## - OAK 1 0.1 8342.4 -32678
## - DAL 1 0.1 8342.4 -32678
## - SEA 1 0.1 8342.4 -32678
## - NYJ 1 0.1 8342.4 -32678
## - IND 1 0.1 8342.4 -32678
## - CAR 1 0.1 8342.4 -32678
## - avg_qbtdp_plyr 1 0.1 8342.4 -32678
## - bad_weather_1 1 0.1 8342.4 -32678
## - KC 1 0.1 8342.4 -32678
## - MIA 1 0.2 8342.5 -32678
## - grass_1 1 0.3 8342.6 -32677
## - hot_weather 1 0.3 8342.6 -32677
## - PHI 1 0.4 8342.7 -32677
## - TB 1 0.4 8342.7 -32677
## - TEN 1 0.5 8342.8 -32676
## - MINN 1 0.6 8342.9 -32676
## - NE 1 0.6 8342.9 -32676
## - ATL 1 0.6 8342.9 -32676
## <none> 8342.3 -32676
## - home_team_1 1 0.7 8343.0 -32676
## - BAL 1 0.7 8343.0 -32676
## - WAS 1 0.8 8343.1 -32676
## - ARI 1 0.8 8343.1 -32675
## - SD 1 1.0 8343.3 -32675
## - CLE 1 1.3 8343.6 -32674
## - CIN 1 1.3 8343.6 -32674
## - DET 1 1.6 8343.9 -32673
## - HOU 1 1.8 8344.1 -32672
## - STL 1 1.8 8344.1 -32672
## - NYG 1 2.1 8344.4 -32671
## - cold_weather 1 3.5 8345.8 -32667
## - DEN 1 3.6 8345.9 -32666
## - forty1 1 6.8 8349.1 -32656
## - avg_rbry_pos 1 26.5 8368.8 -32591
## - avg_rbry_plyr 1 7477.5 15819.8 -15091
##
## Step: AIC=-32678.18
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - GB 1 0.0 8342.3 -32680
## - BUF 1 0.0 8342.3 -32680
## - weight 1 0.0 8342.3 -32680
## - PIT 1 0.0 8342.3 -32680
## - avg_fuml_plyr 1 0.0 8342.3 -32680
## - height 1 0.0 8342.3 -32680
## - avg_rectd_plyr 1 0.0 8342.3 -32680
## - NOR 1 0.1 8342.4 -32680
## - JAC 1 0.1 8342.4 -32680
## - CHI 1 0.1 8342.4 -32680
## - OAK 1 0.1 8342.4 -32680
## - DAL 1 0.1 8342.4 -32680
## - SEA 1 0.1 8342.4 -32680
## - NYJ 1 0.1 8342.4 -32680
## - IND 1 0.1 8342.4 -32680
## - CAR 1 0.1 8342.4 -32680
## - avg_qbtdp_plyr 1 0.1 8342.4 -32680
## - bad_weather_1 1 0.1 8342.4 -32680
## - KC 1 0.1 8342.4 -32680
## - MIA 1 0.2 8342.5 -32680
## - grass_1 1 0.3 8342.6 -32679
## - hot_weather 1 0.3 8342.6 -32679
## - PHI 1 0.4 8342.7 -32679
## - TB 1 0.4 8342.7 -32679
## - TEN 1 0.5 8342.8 -32678
## - MINN 1 0.6 8342.9 -32678
## - NE 1 0.6 8342.9 -32678
## - ATL 1 0.6 8342.9 -32678
## <none> 8342.3 -32678
## - home_team_1 1 0.7 8343.0 -32678
## - BAL 1 0.7 8343.0 -32678
## - WAS 1 0.8 8343.1 -32678
## - ARI 1 0.8 8343.1 -32677
## - SD 1 1.0 8343.3 -32677
## - CLE 1 1.3 8343.6 -32676
## - CIN 1 1.3 8343.6 -32676
## - DET 1 1.6 8343.9 -32675
## - HOU 1 1.8 8344.1 -32674
## - STL 1 1.8 8344.1 -32674
## - NYG 1 2.1 8344.4 -32673
## - cold_weather 1 3.5 8345.8 -32669
## - DEN 1 3.6 8345.9 -32668
## - forty1 1 9.1 8351.4 -32650
## - avg_rbry_pos 1 26.5 8368.8 -32593
## - avg_rbry_plyr 1 7498.1 15840.4 -15057
##
## Step: AIC=-32680.17
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PIT 1 0.0 8342.3 -32682
## - weight 1 0.0 8342.3 -32682
## - avg_fuml_plyr 1 0.0 8342.3 -32682
## - BUF 1 0.0 8342.3 -32682
## - height 1 0.0 8342.3 -32682
## - avg_rectd_plyr 1 0.0 8342.4 -32682
## - JAC 1 0.1 8342.4 -32682
## - CHI 1 0.1 8342.4 -32682
## - OAK 1 0.1 8342.4 -32682
## - DAL 1 0.1 8342.4 -32682
## - NOR 1 0.1 8342.4 -32682
## - avg_qbtdp_plyr 1 0.1 8342.4 -32682
## - IND 1 0.1 8342.4 -32682
## - bad_weather_1 1 0.1 8342.4 -32682
## - SEA 1 0.2 8342.5 -32682
## - NYJ 1 0.2 8342.5 -32682
## - CAR 1 0.2 8342.5 -32682
## - KC 1 0.2 8342.5 -32681
## - MIA 1 0.2 8342.5 -32681
## - grass_1 1 0.3 8342.6 -32681
## - hot_weather 1 0.3 8342.6 -32681
## - TB 1 0.5 8342.8 -32681
## - PHI 1 0.5 8342.8 -32680
## <none> 8342.3 -32680
## - TEN 1 0.6 8342.9 -32680
## - home_team_1 1 0.7 8343.0 -32680
## - ATL 1 0.7 8343.0 -32680
## - NE 1 0.7 8343.0 -32680
## - MINN 1 0.8 8343.1 -32680
## - BAL 1 0.8 8343.2 -32679
## - WAS 1 0.9 8343.3 -32679
## - ARI 1 1.0 8343.3 -32679
## - SD 1 1.2 8343.5 -32678
## - CLE 1 1.6 8343.9 -32677
## - CIN 1 1.6 8344.0 -32677
## - DET 1 2.0 8344.3 -32676
## - HOU 1 2.3 8344.6 -32675
## - STL 1 2.3 8344.6 -32675
## - NYG 1 2.7 8345.0 -32673
## - cold_weather 1 3.5 8345.8 -32671
## - DEN 1 4.7 8347.0 -32667
## - forty1 1 9.1 8351.4 -32652
## - avg_rbry_pos 1 26.6 8368.9 -32595
## - avg_rbry_plyr 1 7498.1 15840.4 -15059
##
## Step: AIC=-32682.13
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + SD + SEA + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - weight 1 0.0 8342.3 -32684
## - avg_fuml_plyr 1 0.0 8342.3 -32684
## - height 1 0.0 8342.4 -32684
## - avg_rectd_plyr 1 0.0 8342.4 -32684
## - BUF 1 0.0 8342.4 -32684
## - JAC 1 0.1 8342.4 -32684
## - CHI 1 0.1 8342.4 -32684
## - OAK 1 0.1 8342.4 -32684
## - DAL 1 0.1 8342.4 -32684
## - IND 1 0.1 8342.4 -32684
## - avg_qbtdp_plyr 1 0.1 8342.4 -32684
## - NOR 1 0.1 8342.4 -32684
## - bad_weather_1 1 0.1 8342.5 -32684
## - MIA 1 0.2 8342.5 -32683
## - SEA 1 0.2 8342.5 -32683
## - NYJ 1 0.2 8342.5 -32683
## - CAR 1 0.2 8342.6 -32683
## - KC 1 0.3 8342.6 -32683
## - grass_1 1 0.3 8342.6 -32683
## - hot_weather 1 0.3 8342.7 -32683
## - TB 1 0.5 8342.8 -32683
## <none> 8342.3 -32682
## - PHI 1 0.6 8343.0 -32682
## - TEN 1 0.7 8343.0 -32682
## - home_team_1 1 0.7 8343.0 -32682
## - ATL 1 0.7 8343.0 -32682
## - NE 1 0.7 8343.0 -32682
## - BAL 1 0.9 8343.2 -32681
## - MINN 1 1.0 8343.3 -32681
## - WAS 1 1.0 8343.3 -32681
## - ARI 1 1.0 8343.4 -32681
## - SD 1 1.3 8343.6 -32680
## - CLE 1 1.7 8344.0 -32679
## - CIN 1 1.7 8344.1 -32678
## - DET 1 2.1 8344.5 -32677
## - HOU 1 2.4 8344.7 -32676
## - STL 1 2.4 8344.7 -32676
## - NYG 1 2.8 8345.2 -32675
## - cold_weather 1 3.6 8345.9 -32672
## - DEN 1 5.1 8347.4 -32667
## - forty1 1 9.1 8351.4 -32654
## - avg_rbry_pos 1 26.6 8368.9 -32597
## - avg_rbry_plyr 1 7500.2 15842.6 -15057
##
## Step: AIC=-32684.09
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_fuml_plyr 1 0.0 8342.4 -32686
## - BUF 1 0.0 8342.4 -32686
## - avg_rectd_plyr 1 0.0 8342.4 -32686
## - JAC 1 0.1 8342.4 -32686
## - CHI 1 0.1 8342.4 -32686
## - OAK 1 0.1 8342.4 -32686
## - DAL 1 0.1 8342.4 -32686
## - avg_qbtdp_plyr 1 0.1 8342.4 -32686
## - IND 1 0.1 8342.5 -32686
## - NOR 1 0.1 8342.5 -32686
## - bad_weather_1 1 0.1 8342.5 -32686
## - height 1 0.1 8342.5 -32686
## - MIA 1 0.2 8342.5 -32685
## - NYJ 1 0.2 8342.6 -32685
## - SEA 1 0.2 8342.6 -32685
## - CAR 1 0.3 8342.6 -32685
## - KC 1 0.3 8342.6 -32685
## - grass_1 1 0.3 8342.6 -32685
## - hot_weather 1 0.3 8342.7 -32685
## - TB 1 0.5 8342.8 -32685
## <none> 8342.3 -32684
## - PHI 1 0.6 8343.0 -32684
## - home_team_1 1 0.7 8343.0 -32684
## - TEN 1 0.7 8343.0 -32684
## - ATL 1 0.7 8343.1 -32684
## - NE 1 0.7 8343.1 -32684
## - BAL 1 0.9 8343.2 -32683
## - MINN 1 1.0 8343.3 -32683
## - WAS 1 1.0 8343.3 -32683
## - ARI 1 1.0 8343.4 -32683
## - SD 1 1.3 8343.6 -32682
## - CLE 1 1.7 8344.0 -32680
## - CIN 1 1.8 8344.1 -32680
## - DET 1 2.1 8344.5 -32679
## - STL 1 2.4 8344.8 -32678
## - HOU 1 2.4 8344.8 -32678
## - NYG 1 2.9 8345.2 -32677
## - cold_weather 1 3.6 8345.9 -32674
## - DEN 1 5.1 8347.4 -32669
## - forty1 1 10.8 8353.2 -32650
## - avg_rbry_pos 1 30.3 8372.7 -32586
## - avg_rbry_plyr 1 7517.1 15859.5 -15030
##
## Step: AIC=-32686
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.0 8342.4 -32688
## - avg_rectd_plyr 1 0.0 8342.4 -32688
## - JAC 1 0.1 8342.4 -32688
## - OAK 1 0.1 8342.4 -32688
## - CHI 1 0.1 8342.4 -32688
## - DAL 1 0.1 8342.4 -32688
## - avg_qbtdp_plyr 1 0.1 8342.5 -32688
## - IND 1 0.1 8342.5 -32688
## - NOR 1 0.1 8342.5 -32688
## - bad_weather_1 1 0.1 8342.5 -32688
## - height 1 0.1 8342.5 -32688
## - NYJ 1 0.2 8342.6 -32687
## - MIA 1 0.2 8342.6 -32687
## - SEA 1 0.2 8342.6 -32687
## - CAR 1 0.2 8342.6 -32687
## - KC 1 0.3 8342.6 -32687
## - grass_1 1 0.3 8342.7 -32687
## - hot_weather 1 0.3 8342.7 -32687
## - TB 1 0.5 8342.8 -32686
## <none> 8342.4 -32686
## - PHI 1 0.6 8343.0 -32686
## - home_team_1 1 0.7 8343.0 -32686
## - TEN 1 0.7 8343.0 -32686
## - ATL 1 0.7 8343.1 -32686
## - NE 1 0.7 8343.1 -32686
## - BAL 1 0.9 8343.2 -32685
## - MINN 1 0.9 8343.3 -32685
## - WAS 1 1.0 8343.4 -32685
## - ARI 1 1.1 8343.4 -32685
## - SD 1 1.3 8343.7 -32684
## - CLE 1 1.7 8344.1 -32682
## - CIN 1 1.8 8344.1 -32682
## - DET 1 2.1 8344.5 -32681
## - HOU 1 2.4 8344.8 -32680
## - STL 1 2.4 8344.8 -32680
## - NYG 1 2.9 8345.2 -32679
## - cold_weather 1 3.5 8345.9 -32676
## - DEN 1 5.1 8347.5 -32671
## - forty1 1 10.8 8353.2 -32652
## - avg_rbry_pos 1 30.3 8372.7 -32588
## - avg_rbry_plyr 1 8447.5 16789.9 -13465
##
## Step: AIC=-32687.88
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_rectd_plyr 1 0.0 8342.4 -32690
## - avg_qbtdp_plyr 1 0.1 8342.5 -32690
## - JAC 1 0.1 8342.5 -32690
## - OAK 1 0.1 8342.5 -32690
## - CHI 1 0.1 8342.5 -32690
## - NOR 1 0.1 8342.5 -32690
## - DAL 1 0.1 8342.5 -32690
## - bad_weather_1 1 0.1 8342.5 -32689
## - height 1 0.2 8342.6 -32689
## - IND 1 0.2 8342.6 -32689
## - NYJ 1 0.2 8342.6 -32689
## - SEA 1 0.2 8342.6 -32689
## - CAR 1 0.2 8342.6 -32689
## - KC 1 0.2 8342.6 -32689
## - grass_1 1 0.3 8342.7 -32689
## - MIA 1 0.3 8342.7 -32689
## - hot_weather 1 0.3 8342.7 -32689
## - TB 1 0.6 8343.0 -32688
## - PHI 1 0.6 8343.0 -32688
## <none> 8342.4 -32688
## - home_team_1 1 0.7 8343.1 -32688
## - TEN 1 0.8 8343.2 -32687
## - ATL 1 0.8 8343.2 -32687
## - NE 1 0.9 8343.3 -32687
## - MINN 1 0.9 8343.3 -32687
## - BAL 1 1.0 8343.4 -32686
## - WAS 1 1.1 8343.5 -32686
## - ARI 1 1.2 8343.6 -32686
## - SD 1 1.5 8343.9 -32685
## - CLE 1 2.0 8344.4 -32683
## - CIN 1 2.0 8344.4 -32683
## - DET 1 2.4 8344.8 -32682
## - HOU 1 2.8 8345.2 -32681
## - STL 1 2.8 8345.2 -32681
## - NYG 1 3.2 8345.6 -32679
## - cold_weather 1 3.5 8346.0 -32678
## - DEN 1 5.6 8348.0 -32671
## - forty1 1 10.9 8353.3 -32654
## - avg_rbry_pos 1 30.3 8372.7 -32590
## - avg_rbry_plyr 1 8448.2 16790.6 -13466
##
## Step: AIC=-32689.77
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_qbtdp_plyr 1 0.1 8342.5 -32692
## - JAC 1 0.1 8342.5 -32691
## - OAK 1 0.1 8342.5 -32691
## - CHI 1 0.1 8342.5 -32691
## - NOR 1 0.1 8342.5 -32691
## - DAL 1 0.1 8342.5 -32691
## - bad_weather_1 1 0.1 8342.6 -32691
## - IND 1 0.2 8342.6 -32691
## - NYJ 1 0.2 8342.6 -32691
## - height 1 0.2 8342.6 -32691
## - SEA 1 0.2 8342.6 -32691
## - CAR 1 0.2 8342.6 -32691
## - KC 1 0.2 8342.7 -32691
## - grass_1 1 0.3 8342.7 -32691
## - MIA 1 0.3 8342.7 -32691
## - hot_weather 1 0.3 8342.8 -32691
## - TB 1 0.6 8343.0 -32690
## - PHI 1 0.6 8343.0 -32690
## <none> 8342.4 -32690
## - home_team_1 1 0.7 8343.1 -32690
## - TEN 1 0.8 8343.2 -32689
## - ATL 1 0.8 8343.3 -32689
## - NE 1 0.8 8343.3 -32689
## - MINN 1 0.9 8343.3 -32689
## - BAL 1 1.1 8343.5 -32688
## - WAS 1 1.2 8343.6 -32688
## - ARI 1 1.3 8343.7 -32688
## - SD 1 1.5 8343.9 -32687
## - CLE 1 2.0 8344.4 -32685
## - CIN 1 2.0 8344.5 -32685
## - DET 1 2.4 8344.9 -32684
## - HOU 1 2.8 8345.2 -32683
## - STL 1 2.8 8345.3 -32682
## - NYG 1 3.2 8345.7 -32681
## - cold_weather 1 3.6 8346.0 -32680
## - DEN 1 5.6 8348.1 -32673
## - forty1 1 11.5 8354.0 -32654
## - avg_rbry_pos 1 34.6 8377.0 -32578
## - avg_rbry_plyr 1 8450.6 16793.0 -13464
##
## Step: AIC=-32691.55
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - JAC 1 0.1 8342.6 -32693
## - OAK 1 0.1 8342.6 -32693
## - CHI 1 0.1 8342.6 -32693
## - DAL 1 0.1 8342.6 -32693
## - NOR 1 0.1 8342.6 -32693
## - bad_weather_1 1 0.1 8342.6 -32693
## - IND 1 0.2 8342.7 -32693
## - NYJ 1 0.2 8342.7 -32693
## - SEA 1 0.2 8342.7 -32693
## - height 1 0.2 8342.7 -32693
## - CAR 1 0.2 8342.7 -32693
## - KC 1 0.2 8342.7 -32693
## - grass_1 1 0.3 8342.8 -32693
## - MIA 1 0.3 8342.8 -32693
## - hot_weather 1 0.3 8342.8 -32692
## - PHI 1 0.6 8343.1 -32692
## - TB 1 0.6 8343.1 -32692
## <none> 8342.5 -32692
## - home_team_1 1 0.7 8343.2 -32691
## - TEN 1 0.8 8343.3 -32691
## - ATL 1 0.8 8343.3 -32691
## - NE 1 0.8 8343.3 -32691
## - MINN 1 0.9 8343.4 -32691
## - BAL 1 1.1 8343.6 -32690
## - WAS 1 1.2 8343.7 -32690
## - ARI 1 1.3 8343.8 -32689
## - SD 1 1.5 8344.0 -32689
## - CLE 1 2.0 8344.5 -32687
## - CIN 1 2.0 8344.5 -32687
## - DET 1 2.4 8344.9 -32686
## - HOU 1 2.8 8345.3 -32684
## - STL 1 2.9 8345.4 -32684
## - NYG 1 3.3 8345.8 -32683
## - cold_weather 1 3.6 8346.1 -32682
## - DEN 1 5.6 8348.1 -32675
## - forty1 1 12.9 8355.4 -32651
## - avg_rbry_pos 1 34.6 8377.1 -32580
## - avg_rbry_plyr 1 8496.8 16839.3 -13390
##
## Step: AIC=-32693.25
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.1 8342.7 -32695
## - CHI 1 0.1 8342.7 -32695
## - DAL 1 0.1 8342.7 -32695
## - IND 1 0.1 8342.7 -32695
## - bad_weather_1 1 0.1 8342.7 -32695
## - NOR 1 0.2 8342.8 -32695
## - height 1 0.2 8342.8 -32695
## - NYJ 1 0.2 8342.8 -32695
## - MIA 1 0.2 8342.8 -32694
## - SEA 1 0.2 8342.8 -32694
## - grass_1 1 0.3 8342.9 -32694
## - CAR 1 0.3 8342.9 -32694
## - KC 1 0.3 8342.9 -32694
## - hot_weather 1 0.3 8342.9 -32694
## - TB 1 0.5 8343.1 -32694
## <none> 8342.6 -32693
## - home_team_1 1 0.7 8343.2 -32693
## - PHI 1 0.7 8343.3 -32693
## - TEN 1 0.7 8343.3 -32693
## - ATL 1 0.8 8343.4 -32693
## - NE 1 0.8 8343.4 -32693
## - BAL 1 1.0 8343.6 -32692
## - MINN 1 1.0 8343.6 -32692
## - WAS 1 1.1 8343.7 -32692
## - ARI 1 1.2 8343.8 -32691
## - SD 1 1.4 8344.0 -32691
## - CLE 1 1.9 8344.5 -32689
## - CIN 1 2.0 8344.5 -32689
## - DET 1 2.3 8344.9 -32688
## - HOU 1 2.7 8345.3 -32686
## - STL 1 2.8 8345.4 -32686
## - NYG 1 3.2 8345.8 -32685
## - cold_weather 1 3.5 8346.1 -32684
## - DEN 1 5.5 8348.1 -32677
## - forty1 1 12.9 8355.5 -32653
## - avg_rbry_pos 1 34.6 8377.2 -32581
## - avg_rbry_plyr 1 8497.6 16840.2 -13391
##
## Step: AIC=-32695.01
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI +
## SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CHI 1 0.1 8342.7 -32697
## - DAL 1 0.1 8342.7 -32697
## - IND 1 0.1 8342.8 -32697
## - bad_weather_1 1 0.1 8342.8 -32697
## - height 1 0.2 8342.9 -32696
## - MIA 1 0.2 8342.9 -32696
## - NOR 1 0.2 8342.9 -32696
## - grass_1 1 0.2 8342.9 -32696
## - NYJ 1 0.3 8342.9 -32696
## - SEA 1 0.3 8343.0 -32696
## - CAR 1 0.3 8343.0 -32696
## - hot_weather 1 0.3 8343.0 -32696
## - KC 1 0.4 8343.0 -32696
## - TB 1 0.5 8343.1 -32695
## <none> 8342.7 -32695
## - home_team_1 1 0.6 8343.3 -32695
## - TEN 1 0.7 8343.3 -32695
## - ATL 1 0.7 8343.4 -32695
## - NE 1 0.7 8343.4 -32695
## - PHI 1 0.8 8343.5 -32694
## - BAL 1 0.9 8343.6 -32694
## - WAS 1 1.0 8343.7 -32694
## - ARI 1 1.1 8343.8 -32693
## - MINN 1 1.1 8343.8 -32693
## - SD 1 1.3 8344.0 -32693
## - CLE 1 1.9 8344.5 -32691
## - CIN 1 1.9 8344.5 -32691
## - DET 1 2.3 8344.9 -32690
## - HOU 1 2.7 8345.3 -32688
## - STL 1 2.7 8345.4 -32688
## - NYG 1 3.1 8345.8 -32687
## - cold_weather 1 3.4 8346.1 -32686
## - DEN 1 5.5 8348.2 -32679
## - forty1 1 12.9 8355.5 -32655
## - avg_rbry_pos 1 35.0 8377.6 -32582
## - avg_rbry_plyr 1 8510.3 16852.9 -13372
##
## Step: AIC=-32696.84
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DAL + DEN + DET + HOU +
## IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD +
## SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DAL 1 0.0 8342.8 -32699
## - IND 1 0.1 8342.8 -32699
## - bad_weather_1 1 0.1 8342.8 -32698
## - MIA 1 0.2 8342.9 -32698
## - height 1 0.2 8342.9 -32698
## - grass_1 1 0.2 8343.0 -32698
## - NOR 1 0.2 8343.0 -32698
## - NYJ 1 0.3 8343.0 -32698
## - SEA 1 0.3 8343.1 -32698
## - hot_weather 1 0.3 8343.1 -32698
## - CAR 1 0.4 8343.1 -32698
## - KC 1 0.4 8343.1 -32698
## - TB 1 0.4 8343.2 -32697
## <none> 8342.7 -32697
## - TEN 1 0.6 8343.4 -32697
## - home_team_1 1 0.6 8343.4 -32697
## - ATL 1 0.7 8343.4 -32697
## - NE 1 0.7 8343.4 -32697
## - PHI 1 0.9 8343.6 -32696
## - BAL 1 0.9 8343.6 -32696
## - WAS 1 1.0 8343.7 -32696
## - ARI 1 1.1 8343.8 -32695
## - MINN 1 1.2 8343.9 -32695
## - SD 1 1.3 8344.0 -32695
## - CLE 1 1.8 8344.5 -32693
## - CIN 1 1.8 8344.6 -32693
## - DET 1 2.2 8344.9 -32692
## - HOU 1 2.6 8345.3 -32690
## - STL 1 2.6 8345.4 -32690
## - NYG 1 3.0 8345.8 -32689
## - cold_weather 1 3.5 8346.2 -32687
## - DEN 1 5.4 8348.2 -32681
## - forty1 1 12.9 8355.6 -32657
## - avg_rbry_pos 1 34.9 8377.6 -32584
## - avg_rbry_plyr 1 8514.0 16856.7 -13368
##
## Step: AIC=-32698.69
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + IND +
## KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA +
## STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - IND 1 0.1 8342.8 -32700
## - bad_weather_1 1 0.1 8342.9 -32700
## - MIA 1 0.2 8342.9 -32700
## - height 1 0.2 8343.0 -32700
## - grass_1 1 0.3 8343.0 -32700
## - NOR 1 0.3 8343.0 -32700
## - hot_weather 1 0.3 8343.1 -32700
## - NYJ 1 0.4 8343.1 -32700
## - SEA 1 0.4 8343.1 -32699
## - TB 1 0.4 8343.2 -32699
## - CAR 1 0.4 8343.2 -32699
## - KC 1 0.4 8343.2 -32699
## <none> 8342.8 -32699
## - TEN 1 0.6 8343.4 -32699
## - home_team_1 1 0.6 8343.4 -32699
## - ATL 1 0.6 8343.4 -32699
## - NE 1 0.6 8343.4 -32699
## - BAL 1 0.8 8343.6 -32698
## - WAS 1 0.9 8343.7 -32698
## - PHI 1 0.9 8343.7 -32698
## - ARI 1 1.0 8343.8 -32697
## - SD 1 1.2 8344.0 -32697
## - MINN 1 1.3 8344.1 -32696
## - CLE 1 1.8 8344.5 -32695
## - CIN 1 1.8 8344.6 -32695
## - DET 1 2.2 8344.9 -32694
## - HOU 1 2.6 8345.3 -32692
## - STL 1 2.6 8345.4 -32692
## - NYG 1 3.0 8345.8 -32691
## - cold_weather 1 3.4 8346.2 -32689
## - DEN 1 5.4 8348.2 -32683
## - forty1 1 12.9 8355.6 -32658
## - avg_rbry_pos 1 34.9 8377.7 -32586
## - avg_rbry_plyr 1 8515.5 16858.3 -13367
##
## Step: AIC=-32700.49
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL +
## TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - bad_weather_1 1 0.1 8342.9 -32702
## - MIA 1 0.1 8343.0 -32702
## - height 1 0.2 8343.0 -32702
## - grass_1 1 0.3 8343.1 -32701
## - NOR 1 0.3 8343.2 -32701
## - hot_weather 1 0.3 8343.2 -32701
## - TB 1 0.4 8343.2 -32701
## - NYJ 1 0.4 8343.2 -32701
## - SEA 1 0.4 8343.3 -32701
## - CAR 1 0.5 8343.3 -32701
## - KC 1 0.5 8343.3 -32701
## - TEN 1 0.6 8343.4 -32701
## - home_team_1 1 0.6 8343.4 -32701
## - ATL 1 0.6 8343.4 -32701
## - NE 1 0.6 8343.4 -32701
## <none> 8342.8 -32700
## - BAL 1 0.8 8343.6 -32700
## - WAS 1 0.9 8343.7 -32700
## - PHI 1 1.0 8343.8 -32699
## - ARI 1 1.0 8343.8 -32699
## - SD 1 1.2 8344.0 -32699
## - MINN 1 1.4 8344.2 -32698
## - CLE 1 1.7 8344.6 -32697
## - CIN 1 1.7 8344.6 -32697
## - DET 1 2.1 8344.9 -32696
## - HOU 1 2.5 8345.3 -32694
## - STL 1 2.5 8345.4 -32694
## - NYG 1 2.9 8345.8 -32693
## - cold_weather 1 3.4 8346.2 -32691
## - DEN 1 5.3 8348.2 -32685
## - forty1 1 12.9 8355.7 -32660
## - avg_rbry_pos 1 34.8 8377.7 -32588
## - avg_rbry_plyr 1 8515.5 16858.3 -13369
##
## Step: AIC=-32702.07
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL +
## TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.1 8343.1 -32704
## - height 1 0.2 8343.1 -32703
## - grass_1 1 0.3 8343.2 -32703
## - NOR 1 0.3 8343.3 -32703
## - hot_weather 1 0.4 8343.3 -32703
## - TB 1 0.4 8343.3 -32703
## - NYJ 1 0.4 8343.3 -32703
## - SEA 1 0.4 8343.4 -32703
## - CAR 1 0.5 8343.4 -32703
## - KC 1 0.5 8343.4 -32702
## - TEN 1 0.6 8343.5 -32702
## - ATL 1 0.6 8343.5 -32702
## - home_team_1 1 0.6 8343.5 -32702
## <none> 8342.9 -32702
## - NE 1 0.6 8343.6 -32702
## - BAL 1 0.8 8343.7 -32701
## - WAS 1 0.9 8343.8 -32701
## - ARI 1 1.0 8343.9 -32701
## - PHI 1 1.0 8344.0 -32701
## - SD 1 1.2 8344.1 -32700
## - MINN 1 1.4 8344.4 -32699
## - CIN 1 1.7 8344.7 -32698
## - CLE 1 1.7 8344.7 -32698
## - DET 1 2.1 8345.1 -32697
## - STL 1 2.5 8345.5 -32696
## - HOU 1 2.5 8345.5 -32696
## - NYG 1 3.0 8345.9 -32694
## - cold_weather 1 3.7 8346.6 -32692
## - DEN 1 5.3 8348.2 -32687
## - forty1 1 12.9 8355.9 -32662
## - avg_rbry_pos 1 34.9 8377.8 -32589
## - avg_rbry_plyr 1 8515.9 16858.8 -13370
##
## Step: AIC=-32703.65
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC +
## MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB +
## TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
##
## Df Sum of Sq RSS AIC
## - height 1 0.2 8343.3 -32705
## - grass_1 1 0.3 8343.4 -32705
## - TB 1 0.3 8343.4 -32705
## - hot_weather 1 0.4 8343.4 -32704
## - NOR 1 0.4 8343.5 -32704
## - NYJ 1 0.4 8343.5 -32704
## - SEA 1 0.5 8343.6 -32704
## - TEN 1 0.5 8343.6 -32704
## - CAR 1 0.5 8343.6 -32704
## - ATL 1 0.5 8343.6 -32704
## - KC 1 0.5 8343.6 -32704
## - NE 1 0.6 8343.6 -32704
## <none> 8343.1 -32704
## - home_team_1 1 0.6 8343.7 -32704
## - BAL 1 0.7 8343.8 -32703
## - WAS 1 0.8 8343.9 -32703
## - ARI 1 0.9 8344.0 -32703
## - PHI 1 1.1 8344.2 -32702
## - SD 1 1.1 8344.2 -32702
## - MINN 1 1.5 8344.6 -32701
## - CIN 1 1.7 8344.7 -32700
## - CLE 1 1.7 8344.8 -32700
## - DET 1 2.0 8345.1 -32699
## - STL 1 2.4 8345.5 -32698
## - HOU 1 2.4 8345.5 -32698
## - NYG 1 2.9 8345.9 -32696
## - cold_weather 1 3.6 8346.7 -32694
## - DEN 1 5.2 8348.3 -32689
## - forty1 1 13.0 8356.0 -32663
## - avg_rbry_pos 1 34.9 8378.0 -32591
## - avg_rbry_plyr 1 8517.7 16860.7 -13369
##
## Step: AIC=-32705
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN +
## WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 0.3 8343.6 -32706
## - TB 1 0.3 8343.6 -32706
## - hot_weather 1 0.4 8343.6 -32706
## - NOR 1 0.4 8343.6 -32706
## - NYJ 1 0.4 8343.7 -32706
## - SEA 1 0.5 8343.7 -32705
## - TEN 1 0.5 8343.8 -32705
## - CAR 1 0.5 8343.8 -32705
## - KC 1 0.5 8343.8 -32705
## - ATL 1 0.6 8343.8 -32705
## <none> 8343.3 -32705
## - home_team_1 1 0.6 8343.9 -32705
## - NE 1 0.6 8343.9 -32705
## - BAL 1 0.7 8344.0 -32705
## - WAS 1 0.9 8344.1 -32704
## - ARI 1 0.9 8344.2 -32704
## - PHI 1 1.1 8344.3 -32704
## - SD 1 1.1 8344.4 -32703
## - MINN 1 1.5 8344.8 -32702
## - CIN 1 1.7 8345.0 -32701
## - CLE 1 1.7 8345.0 -32701
## - DET 1 2.0 8345.3 -32700
## - HOU 1 2.4 8345.7 -32699
## - STL 1 2.5 8345.7 -32699
## - NYG 1 2.9 8346.1 -32698
## - cold_weather 1 3.6 8346.9 -32695
## - DEN 1 5.2 8348.5 -32690
## - forty1 1 15.4 8358.7 -32656
## - avg_rbry_pos 1 45.2 8388.4 -32559
## - avg_rbry_plyr 1 8556.5 16899.8 -13307
##
## Step: AIC=-32706.08
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN +
## WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - NOR 1 0.3 8343.9 -32707
## - TB 1 0.3 8343.9 -32707
## - NYJ 1 0.4 8343.9 -32707
## - SEA 1 0.4 8343.9 -32707
## - hot_weather 1 0.4 8344.0 -32707
## - TEN 1 0.5 8344.0 -32707
## - home_team_1 1 0.5 8344.0 -32706
## - CAR 1 0.6 8344.1 -32706
## - KC 1 0.6 8344.2 -32706
## <none> 8343.6 -32706
## - ATL 1 0.6 8344.2 -32706
## - NE 1 0.8 8344.3 -32706
## - BAL 1 0.8 8344.4 -32705
## - WAS 1 0.8 8344.4 -32705
## - ARI 1 1.0 8344.5 -32705
## - SD 1 1.0 8344.6 -32705
## - PHI 1 1.1 8344.7 -32704
## - MINN 1 1.4 8345.0 -32703
## - CLE 1 1.6 8345.2 -32703
## - CIN 1 1.9 8345.4 -32702
## - DET 1 2.2 8345.7 -32701
## - HOU 1 2.6 8346.1 -32700
## - STL 1 2.6 8346.2 -32699
## - NYG 1 3.1 8346.7 -32698
## - cold_weather 1 3.5 8347.1 -32696
## - DEN 1 5.1 8348.7 -32691
## - forty1 1 15.4 8359.0 -32657
## - avg_rbry_pos 1 45.1 8388.7 -32560
## - avg_rbry_plyr 1 8556.7 16900.2 -13309
##
## Step: AIC=-32707.06
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + WAS +
## avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - NYJ 1 0.3 8344.2 -32708
## - SEA 1 0.3 8344.2 -32708
## - TB 1 0.4 8344.2 -32708
## - hot_weather 1 0.4 8344.3 -32708
## - CAR 1 0.5 8344.4 -32707
## - KC 1 0.5 8344.4 -32707
## - home_team_1 1 0.5 8344.4 -32707
## - TEN 1 0.6 8344.4 -32707
## <none> 8343.9 -32707
## - ATL 1 0.7 8344.6 -32707
## - NE 1 0.9 8344.7 -32706
## - BAL 1 0.9 8344.8 -32706
## - WAS 1 0.9 8344.8 -32706
## - PHI 1 1.0 8344.9 -32706
## - ARI 1 1.1 8345.0 -32705
## - SD 1 1.2 8345.0 -32705
## - MINN 1 1.3 8345.2 -32705
## - CLE 1 1.8 8345.6 -32703
## - CIN 1 2.0 8345.9 -32702
## - DET 1 2.4 8346.3 -32701
## - HOU 1 2.8 8346.6 -32700
## - STL 1 2.8 8346.7 -32700
## - NYG 1 3.3 8347.2 -32698
## - cold_weather 1 3.6 8347.5 -32697
## - DEN 1 5.4 8349.2 -32691
## - forty1 1 15.5 8359.3 -32658
## - avg_rbry_pos 1 44.9 8388.8 -32561
## - avg_rbry_plyr 1 8570.1 16914.0 -13289
##
## Step: AIC=-32708.07
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NYG + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.3 8344.4 -32709
## - CAR 1 0.4 8344.6 -32709
## - TB 1 0.4 8344.6 -32709
## - hot_weather 1 0.4 8344.6 -32709
## - KC 1 0.5 8344.6 -32709
## - home_team_1 1 0.5 8344.7 -32708
## <none> 8344.2 -32708
## - TEN 1 0.6 8344.8 -32708
## - ATL 1 0.8 8345.0 -32707
## - PHI 1 0.9 8345.1 -32707
## - NE 1 1.0 8345.1 -32707
## - BAL 1 1.0 8345.2 -32707
## - WAS 1 1.0 8345.2 -32707
## - MINN 1 1.2 8345.4 -32706
## - ARI 1 1.2 8345.4 -32706
## - SD 1 1.3 8345.4 -32706
## - CLE 1 1.9 8346.1 -32704
## - CIN 1 2.2 8346.4 -32703
## - DET 1 2.5 8346.7 -32702
## - HOU 1 2.9 8347.1 -32700
## - STL 1 3.0 8347.2 -32700
## - NYG 1 3.5 8347.7 -32698
## - cold_weather 1 3.6 8347.7 -32698
## - DEN 1 5.7 8349.8 -32691
## - forty1 1 15.5 8359.6 -32659
## - avg_rbry_pos 1 45.1 8389.2 -32562
## - avg_rbry_plyr 1 8572.8 16917.0 -13286
##
## Step: AIC=-32709.21
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - CAR 1 0.4 8344.8 -32710
## - KC 1 0.4 8344.8 -32710
## - hot_weather 1 0.5 8344.9 -32710
## - TB 1 0.5 8344.9 -32710
## - home_team_1 1 0.5 8344.9 -32710
## <none> 8344.4 -32709
## - TEN 1 0.7 8345.1 -32709
## - PHI 1 0.9 8345.3 -32708
## - ATL 1 0.9 8345.3 -32708
## - NE 1 1.1 8345.5 -32708
## - BAL 1 1.1 8345.5 -32708
## - WAS 1 1.1 8345.6 -32707
## - MINN 1 1.1 8345.6 -32707
## - ARI 1 1.3 8345.7 -32707
## - SD 1 1.4 8345.8 -32707
## - CLE 1 2.0 8346.5 -32705
## - CIN 1 2.3 8346.8 -32704
## - DET 1 2.7 8347.1 -32702
## - HOU 1 3.1 8347.5 -32701
## - STL 1 3.1 8347.6 -32701
## - cold_weather 1 3.5 8347.9 -32700
## - NYG 1 3.7 8348.2 -32699
## - DEN 1 5.9 8350.3 -32692
## - forty1 1 15.6 8360.0 -32660
## - avg_rbry_pos 1 45.2 8389.6 -32563
## - avg_rbry_plyr 1 8574.3 16918.7 -13285
##
## Step: AIC=-32709.96
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CIN + CLE + DEN + DET + HOU + KC + MINN + NE +
## NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - KC 1 0.4 8345.2 -32711
## - hot_weather 1 0.5 8345.3 -32710
## - home_team_1 1 0.5 8345.3 -32710
## - TB 1 0.6 8345.4 -32710
## <none> 8344.8 -32710
## - TEN 1 0.8 8345.6 -32709
## - PHI 1 0.8 8345.6 -32709
## - ATL 1 1.0 8345.8 -32709
## - MINN 1 1.1 8345.9 -32708
## - NE 1 1.2 8346.0 -32708
## - BAL 1 1.2 8346.0 -32708
## - WAS 1 1.2 8346.0 -32708
## - ARI 1 1.4 8346.2 -32707
## - SD 1 1.5 8346.3 -32707
## - CLE 1 2.2 8347.0 -32705
## - CIN 1 2.5 8347.3 -32704
## - DET 1 2.8 8347.6 -32703
## - HOU 1 3.2 8348.0 -32701
## - STL 1 3.3 8348.1 -32701
## - cold_weather 1 3.5 8348.3 -32700
## - NYG 1 3.9 8348.7 -32699
## - DEN 1 6.2 8351.0 -32692
## - forty1 1 15.6 8360.4 -32661
## - avg_rbry_pos 1 45.4 8390.2 -32563
## - avg_rbry_plyr 1 8575.7 16920.5 -13284
##
## Step: AIC=-32710.78
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CIN + CLE + DEN + DET + HOU + MINN + NE + NYG +
## PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.4 8345.6 -32711
## - home_team_1 1 0.4 8345.6 -32711
## <none> 8345.2 -32711
## - TB 1 0.6 8345.8 -32711
## - PHI 1 0.7 8345.9 -32710
## - TEN 1 0.9 8346.0 -32710
## - MINN 1 1.0 8346.1 -32710
## - ATL 1 1.1 8346.2 -32709
## - NE 1 1.3 8346.4 -32709
## - BAL 1 1.3 8346.5 -32709
## - WAS 1 1.3 8346.5 -32708
## - ARI 1 1.5 8346.7 -32708
## - SD 1 1.6 8346.7 -32708
## - CLE 1 2.3 8347.5 -32705
## - CIN 1 2.6 8347.8 -32704
## - DET 1 2.9 8348.1 -32703
## - HOU 1 3.4 8348.5 -32702
## - STL 1 3.4 8348.6 -32701
## - cold_weather 1 3.5 8348.6 -32701
## - NYG 1 4.1 8349.3 -32699
## - DEN 1 6.4 8351.6 -32692
## - forty1 1 15.6 8360.8 -32661
## - avg_rbry_pos 1 45.3 8390.5 -32564
## - avg_rbry_plyr 1 8575.8 16921.0 -13285
##
## Step: AIC=-32711.31
## ra ~ cold_weather + home_team_1 + forty1 + ARI + ATL + BAL +
## CIN + CLE + DEN + DET + HOU + MINN + NE + NYG + PHI + SD +
## STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - home_team_1 1 0.4 8346.0 -32712
## - TB 1 0.6 8346.2 -32711
## <none> 8345.6 -32711
## - PHI 1 0.7 8346.3 -32711
## - TEN 1 0.9 8346.5 -32710
## - MINN 1 1.0 8346.6 -32710
## - ATL 1 1.1 8346.7 -32710
## - NE 1 1.3 8346.9 -32709
## - BAL 1 1.3 8346.9 -32709
## - WAS 1 1.3 8347.0 -32709
## - SD 1 1.5 8347.1 -32708
## - ARI 1 1.5 8347.1 -32708
## - CLE 1 2.3 8347.9 -32706
## - CIN 1 2.6 8348.2 -32705
## - DET 1 3.0 8348.6 -32704
## - STL 1 3.4 8349.0 -32702
## - HOU 1 3.4 8349.0 -32702
## - cold_weather 1 3.5 8349.1 -32702
## - NYG 1 4.1 8349.7 -32700
## - DEN 1 6.4 8352.0 -32692
## - forty1 1 15.7 8361.3 -32662
## - avg_rbry_pos 1 45.4 8391.0 -32564
## - avg_rbry_plyr 1 8575.4 16921.0 -13287
##
## Step: AIC=-32711.86
## ra ~ cold_weather + forty1 + ARI + ATL + BAL + CIN + CLE + DEN +
## DET + HOU + MINN + NE + NYG + PHI + SD + STL + TB + TEN +
## WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## <none> 8346.0 -32712
## - TB 1 0.6 8346.7 -32712
## - PHI 1 0.7 8346.7 -32712
## - TEN 1 0.9 8347.0 -32711
## - ATL 1 0.9 8347.0 -32711
## - MINN 1 1.0 8347.0 -32711
## - NE 1 1.3 8347.4 -32709
## - ARI 1 1.3 8347.4 -32709
## - BAL 1 1.3 8347.4 -32709
## - WAS 1 1.4 8347.5 -32709
## - SD 1 1.5 8347.6 -32709
## - CLE 1 2.4 8348.4 -32706
## - CIN 1 2.7 8348.7 -32705
## - DET 1 2.8 8348.8 -32705
## - STL 1 3.2 8349.2 -32703
## - HOU 1 3.2 8349.2 -32703
## - cold_weather 1 3.8 8349.8 -32701
## - NYG 1 4.2 8350.2 -32700
## - DEN 1 6.5 8352.6 -32692
## - forty1 1 15.6 8361.7 -32662
## - avg_rbry_pos 1 45.4 8391.4 -32565
## - avg_rbry_plyr 1 8575.6 16921.6 -13288TDR
PreProcess:
set.seed(123)
splitdr <- sample.split(nfl_data$tdr, SplitRatio = 0.7)
Traintdr <- subset(nfl_data, split == TRUE)
Testtdr <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Traintdr, method = c("center", "scale"))
trainTransformedtdr <- predict(preProcValues, Traintdr)
testTransformedtdr <- predict(preProcValues, Testtdr)ggpairs:
ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[46:51]))])
regression:
tdrregform <- formula(paste("ra ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegtdr <- lm(tdrregform, data = trainTransformedtdr)
summary(linRegRushAtt)##
## Call:
## lm(formula = raregform, data = trainTransformedra)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8046 -0.0854 -0.0090 0.0496 5.3831
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.104e-15 3.326e-03 0.000 1.000000
## height -2.162e-03 6.453e-03 -0.335 0.737573
## weight -1.279e-03 6.048e-03 -0.212 0.832493
## cold_weather 1.184e-02 3.501e-03 3.381 0.000724 ***
## hot_weather -3.506e-03 3.356e-03 -1.045 0.296176
## home_team_1 5.312e-03 3.619e-03 1.468 0.142168
## forty1 2.705e-02 5.740e-03 4.712 2.46e-06 ***
## vertical1 2.959e-04 4.413e-03 0.067 0.946539
## ARI 7.646e-03 4.653e-03 1.643 0.100312
## ATL 6.424e-03 4.675e-03 1.374 0.169437
## BAL 7.016e-03 4.679e-03 1.499 0.133760
## BUF -8.683e-04 4.619e-03 -0.188 0.850888
## CAR -2.889e-03 4.589e-03 -0.630 0.528932
## CHI 2.194e-03 4.537e-03 0.483 0.628766
## CIN 9.587e-03 4.621e-03 2.075 0.038017 *
## CLE 9.419e-03 4.600e-03 2.048 0.040589 *
## DAL 2.418e-03 4.646e-03 0.521 0.602708
## DEN 1.599e-02 4.664e-03 3.429 0.000607 ***
## DET 1.059e-02 4.600e-03 2.302 0.021340 *
## GB 5.605e-04 4.735e-03 0.118 0.905783
## HOU 1.138e-02 4.679e-03 2.432 0.015023 *
## IND 2.856e-03 4.645e-03 0.615 0.538603
## JAC 2.146e-03 4.531e-03 0.474 0.635752
## KC -3.085e-03 4.630e-03 -0.666 0.505194
## MIA 3.608e-03 4.556e-03 0.792 0.428412
## MINN -6.259e-03 4.584e-03 -1.365 0.172130
## NE 6.544e-03 4.787e-03 1.367 0.171597
## NOR -1.954e-03 4.772e-03 -0.409 0.682181
## NYG 1.218e-02 4.665e-03 2.611 0.009035 **
## NYJ -2.709e-03 4.647e-03 -0.583 0.560015
## OAK 2.270e-03 4.677e-03 0.485 0.627353
## PHI -4.940e-03 4.532e-03 -1.090 0.275639
## PIT 1.039e-03 4.651e-03 0.223 0.823167
## SD 8.241e-03 4.564e-03 1.806 0.070952 .
## SEA -2.708e-03 4.736e-03 -0.572 0.567490
## STL 1.129e-02 4.610e-03 2.449 0.014334 *
## TB 5.189e-03 4.567e-03 1.136 0.255896
## TEN 6.032e-03 4.594e-03 1.313 0.189196
## WAS 7.307e-03 4.619e-03 1.582 0.113631
## avg_trg_team NA NA NA NA
## avg_rectd_plyr -1.540e-03 4.247e-03 -0.363 0.716951
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr 7.971e-01 5.083e-03 156.823 < 2e-16 ***
## avg_rbry_pos 5.532e-02 5.922e-03 9.341 < 2e-16 ***
## avg_fuml_plyr 1.334e-03 4.913e-03 0.271 0.786013
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -3.404e-03 5.337e-03 -0.638 0.523639
## avg_qbtdp_team NA NA NA NA
## grass_1 -3.779e-03 3.827e-03 -0.987 0.323445
## bad_weather_1 2.234e-03 3.383e-03 0.660 0.509067
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5514 on 27438 degrees of freedom
## Multiple R-squared: 0.6965, Adjusted R-squared: 0.696
## F-statistic: 1399 on 45 and 27438 DF, p-value: < 2.2e-16linRegtdr2 <- update(linRegRushYd,~.-height-weight-hot_weather
-home_team_1-age-is_TE-vertical1-ARI-ATL-BAL - BUF - CAR - CHI
-CIN - CLE - DAL - GB - JAC - KC - MIA
-MINN - NE - NOR -NYJ - OAK - PHI - PIT -SD - SEA
-TB - TEN - WAS
-avg_rectd_plyr-avg_trg_team-avg_tdr_team-avg_rbra_team
-avg_fuml_team-avg_fuml_plyr-avg_qbints_team-avg_qbtdp_team-avg_qbints_plyr
-bad_weather_1-grass_1)
summary(linRegtdr2)##
## Call:
## lm(formula = ry ~ cold_weather + forty1 + DEN + DET + HOU + IND +
## NYG + STL + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr,
## data = trainTransformedry)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4809 -0.0756 -0.0161 0.0145 7.1744
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.337e-14 3.912e-03 0.000 1.000000
## cold_weather 1.434e-02 3.940e-03 3.641 0.000272 ***
## forty1 -2.918e-04 4.527e-03 -0.064 0.948609
## DEN 7.798e-03 3.927e-03 1.986 0.047077 *
## DET 4.884e-03 3.935e-03 1.241 0.214576
## HOU 5.955e-03 3.938e-03 1.512 0.130493
## IND -2.975e-03 3.928e-03 -0.757 0.448787
## NYG 6.068e-03 3.931e-03 1.543 0.122723
## STL 4.319e-03 3.931e-03 1.099 0.271837
## avg_rbry_plyr 7.584e-01 5.588e-03 135.721 < 2e-16 ***
## avg_rbry_pos 3.961e-03 5.522e-03 0.717 0.473119
## avg_qbtdp_plyr -1.006e-03 4.461e-03 -0.226 0.821536
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6486 on 27472 degrees of freedom
## Multiple R-squared: 0.5795, Adjusted R-squared: 0.5793
## F-statistic: 3441 on 11 and 27472 DF, p-value: < 2.2e-16linRegtdr3 <- update(linRegtdr2,~.-is_WR-is_TE-forty1-DET-HOU-NYG-STL-avg_rbry_pos)
summary(linRegtdr3)##
## Call:
## lm(formula = ry ~ cold_weather + DEN + IND + avg_rbry_plyr +
## avg_qbtdp_plyr, data = trainTransformedry)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4560 -0.0781 -0.0085 0.0082 7.1710
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.343e-14 3.912e-03 0.000 1.000000
## cold_weather 1.375e-02 3.916e-03 3.512 0.000446 ***
## DEN 7.084e-03 3.917e-03 1.808 0.070553 .
## IND -3.724e-03 3.916e-03 -0.951 0.341701
## avg_rbry_plyr 7.610e-01 3.913e-03 194.482 < 2e-16 ***
## avg_qbtdp_plyr -1.210e-03 3.913e-03 -0.309 0.757208
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6486 on 27478 degrees of freedom
## Multiple R-squared: 0.5794, Adjusted R-squared: 0.5793
## F-statistic: 7569 on 5 and 27478 DF, p-value: < 2.2e-16Testing:
RushTdrPredicted <- predict(linRegtdr3, newdata = testTransformedtdr)
SSErutdr <- sum((RushTdrPredicted - testTransformedtdr$tdr)^2)
SSTrutdr <- sum((mean(nfl_data$tdr)-testTransformedtdr$tdr)^2)
r2_rutdr <- 1 - SSErutdr/SSTrutdr
r2_rutdr## [1] 0.08372787rmse_rutdr <- sqrt(SSErutdr/nrow(testTransformedtdr))
rmse_rutdr## [1] 0.9645189Plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegtdr3, which = c(1:3,2))
Summary Statistics:
confint(linRegtdr3)## 2.5 % 97.5 %
## (Intercept) -0.0076686590 0.007668659
## cold_weather 0.0060761053 0.021427471
## DEN -0.0005940149 0.014762520
## IND -0.0113994186 0.003952273
## avg_rbry_plyr 0.7532922619 0.768630653
## avg_qbtdp_plyr -0.0088797123 0.006460201coef(summary(linRegtdr3))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.342949e-14 0.003912481 5.988396e-12 1.0000000000
## cold_weather 1.375179e-02 0.003916064 3.511635e+00 0.0004460732
## DEN 7.084252e-03 0.003917383 1.808415e+00 0.0705529133
## IND -3.723573e-03 0.003916147 -9.508255e-01 0.3417013100
## avg_rbry_plyr 7.609615e-01 0.003912754 1.944823e+02 0.0000000000
## avg_qbtdp_plyr -1.209756e-03 0.003913143 -3.091520e-01 0.7572082541anova(linRegtdr3)## Analysis of Variance Table
##
## Response: ry
## Df Sum Sq Mean Sq F value Pr(>F)
## cold_weather 1 7.5 7.5 17.7343 2.548e-05 ***
## DEN 1 0.1 0.1 0.3041 0.58133
## IND 1 2.2 2.2 5.2589 0.02184 *
## avg_rbry_plyr 1 15912.8 15912.8 37823.6618 < 2.2e-16 ***
## avg_qbtdp_plyr 1 0.0 0.0 0.0956 0.75721
## Residuals 27478 11560.3 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_ra <- step(lm(tdrregform, data = trainTransformedtdr), direction = "backward")## Start: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 0.0 8342.3 -32678
## - GB 1 0.0 8342.3 -32678
## - BUF 1 0.0 8342.3 -32678
## - weight 1 0.0 8342.3 -32678
## - PIT 1 0.0 8342.3 -32678
## - avg_fuml_plyr 1 0.0 8342.3 -32678
## - height 1 0.0 8342.3 -32678
## - avg_rectd_plyr 1 0.0 8342.3 -32678
## - NOR 1 0.1 8342.4 -32678
## - JAC 1 0.1 8342.4 -32678
## - CHI 1 0.1 8342.4 -32678
## - OAK 1 0.1 8342.4 -32678
## - DAL 1 0.1 8342.4 -32678
## - SEA 1 0.1 8342.4 -32678
## - NYJ 1 0.1 8342.4 -32678
## - IND 1 0.1 8342.4 -32678
## - CAR 1 0.1 8342.4 -32678
## - avg_qbtdp_plyr 1 0.1 8342.4 -32678
## - bad_weather_1 1 0.1 8342.4 -32678
## - KC 1 0.1 8342.4 -32678
## - MIA 1 0.2 8342.5 -32678
## - grass_1 1 0.3 8342.6 -32677
## - hot_weather 1 0.3 8342.6 -32677
## - PHI 1 0.4 8342.7 -32677
## - TB 1 0.4 8342.7 -32677
## - TEN 1 0.5 8342.8 -32676
## - MINN 1 0.6 8342.9 -32676
## - NE 1 0.6 8342.9 -32676
## - ATL 1 0.6 8342.9 -32676
## <none> 8342.3 -32676
## - home_team_1 1 0.7 8343.0 -32676
## - BAL 1 0.7 8343.0 -32676
## - WAS 1 0.8 8343.1 -32676
## - ARI 1 0.8 8343.1 -32675
## - SD 1 1.0 8343.3 -32675
## - CLE 1 1.3 8343.6 -32674
## - CIN 1 1.3 8343.6 -32674
## - DET 1 1.6 8343.9 -32673
## - HOU 1 1.8 8344.1 -32672
## - STL 1 1.8 8344.1 -32672
## - NYG 1 2.1 8344.4 -32671
## - cold_weather 1 3.5 8345.8 -32667
## - DEN 1 3.6 8345.9 -32666
## - forty1 1 6.8 8349.1 -32656
## - avg_rbry_pos 1 26.5 8368.8 -32591
## - avg_rbry_plyr 1 7477.5 15819.8 -15091
##
## Step: AIC=-32678.18
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN +
## NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - GB 1 0.0 8342.3 -32680
## - BUF 1 0.0 8342.3 -32680
## - weight 1 0.0 8342.3 -32680
## - PIT 1 0.0 8342.3 -32680
## - avg_fuml_plyr 1 0.0 8342.3 -32680
## - height 1 0.0 8342.3 -32680
## - avg_rectd_plyr 1 0.0 8342.3 -32680
## - NOR 1 0.1 8342.4 -32680
## - JAC 1 0.1 8342.4 -32680
## - CHI 1 0.1 8342.4 -32680
## - OAK 1 0.1 8342.4 -32680
## - DAL 1 0.1 8342.4 -32680
## - SEA 1 0.1 8342.4 -32680
## - NYJ 1 0.1 8342.4 -32680
## - IND 1 0.1 8342.4 -32680
## - CAR 1 0.1 8342.4 -32680
## - avg_qbtdp_plyr 1 0.1 8342.4 -32680
## - bad_weather_1 1 0.1 8342.4 -32680
## - KC 1 0.1 8342.4 -32680
## - MIA 1 0.2 8342.5 -32680
## - grass_1 1 0.3 8342.6 -32679
## - hot_weather 1 0.3 8342.6 -32679
## - PHI 1 0.4 8342.7 -32679
## - TB 1 0.4 8342.7 -32679
## - TEN 1 0.5 8342.8 -32678
## - MINN 1 0.6 8342.9 -32678
## - NE 1 0.6 8342.9 -32678
## - ATL 1 0.6 8342.9 -32678
## <none> 8342.3 -32678
## - home_team_1 1 0.7 8343.0 -32678
## - BAL 1 0.7 8343.0 -32678
## - WAS 1 0.8 8343.1 -32678
## - ARI 1 0.8 8343.1 -32677
## - SD 1 1.0 8343.3 -32677
## - CLE 1 1.3 8343.6 -32676
## - CIN 1 1.3 8343.6 -32676
## - DET 1 1.6 8343.9 -32675
## - HOU 1 1.8 8344.1 -32674
## - STL 1 1.8 8344.1 -32674
## - NYG 1 2.1 8344.4 -32673
## - cold_weather 1 3.5 8345.8 -32669
## - DEN 1 3.6 8345.9 -32668
## - forty1 1 9.1 8351.4 -32650
## - avg_rbry_pos 1 26.5 8368.8 -32593
## - avg_rbry_plyr 1 7498.1 15840.4 -15057
##
## Step: AIC=-32680.17
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - PIT 1 0.0 8342.3 -32682
## - weight 1 0.0 8342.3 -32682
## - avg_fuml_plyr 1 0.0 8342.3 -32682
## - BUF 1 0.0 8342.3 -32682
## - height 1 0.0 8342.3 -32682
## - avg_rectd_plyr 1 0.0 8342.4 -32682
## - JAC 1 0.1 8342.4 -32682
## - CHI 1 0.1 8342.4 -32682
## - OAK 1 0.1 8342.4 -32682
## - DAL 1 0.1 8342.4 -32682
## - NOR 1 0.1 8342.4 -32682
## - avg_qbtdp_plyr 1 0.1 8342.4 -32682
## - IND 1 0.1 8342.4 -32682
## - bad_weather_1 1 0.1 8342.4 -32682
## - SEA 1 0.2 8342.5 -32682
## - NYJ 1 0.2 8342.5 -32682
## - CAR 1 0.2 8342.5 -32682
## - KC 1 0.2 8342.5 -32681
## - MIA 1 0.2 8342.5 -32681
## - grass_1 1 0.3 8342.6 -32681
## - hot_weather 1 0.3 8342.6 -32681
## - TB 1 0.5 8342.8 -32681
## - PHI 1 0.5 8342.8 -32680
## <none> 8342.3 -32680
## - TEN 1 0.6 8342.9 -32680
## - home_team_1 1 0.7 8343.0 -32680
## - ATL 1 0.7 8343.0 -32680
## - NE 1 0.7 8343.0 -32680
## - MINN 1 0.8 8343.1 -32680
## - BAL 1 0.8 8343.2 -32679
## - WAS 1 0.9 8343.3 -32679
## - ARI 1 1.0 8343.3 -32679
## - SD 1 1.2 8343.5 -32678
## - CLE 1 1.6 8343.9 -32677
## - CIN 1 1.6 8344.0 -32677
## - DET 1 2.0 8344.3 -32676
## - HOU 1 2.3 8344.6 -32675
## - STL 1 2.3 8344.6 -32675
## - NYG 1 2.7 8345.0 -32673
## - cold_weather 1 3.5 8345.8 -32671
## - DEN 1 4.7 8347.0 -32667
## - forty1 1 9.1 8351.4 -32652
## - avg_rbry_pos 1 26.6 8368.9 -32595
## - avg_rbry_plyr 1 7498.1 15840.4 -15059
##
## Step: AIC=-32682.13
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + SD + SEA + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - weight 1 0.0 8342.3 -32684
## - avg_fuml_plyr 1 0.0 8342.3 -32684
## - height 1 0.0 8342.4 -32684
## - avg_rectd_plyr 1 0.0 8342.4 -32684
## - BUF 1 0.0 8342.4 -32684
## - JAC 1 0.1 8342.4 -32684
## - CHI 1 0.1 8342.4 -32684
## - OAK 1 0.1 8342.4 -32684
## - DAL 1 0.1 8342.4 -32684
## - IND 1 0.1 8342.4 -32684
## - avg_qbtdp_plyr 1 0.1 8342.4 -32684
## - NOR 1 0.1 8342.4 -32684
## - bad_weather_1 1 0.1 8342.5 -32684
## - MIA 1 0.2 8342.5 -32683
## - SEA 1 0.2 8342.5 -32683
## - NYJ 1 0.2 8342.5 -32683
## - CAR 1 0.2 8342.6 -32683
## - KC 1 0.3 8342.6 -32683
## - grass_1 1 0.3 8342.6 -32683
## - hot_weather 1 0.3 8342.7 -32683
## - TB 1 0.5 8342.8 -32683
## <none> 8342.3 -32682
## - PHI 1 0.6 8343.0 -32682
## - TEN 1 0.7 8343.0 -32682
## - home_team_1 1 0.7 8343.0 -32682
## - ATL 1 0.7 8343.0 -32682
## - NE 1 0.7 8343.0 -32682
## - BAL 1 0.9 8343.2 -32681
## - MINN 1 1.0 8343.3 -32681
## - WAS 1 1.0 8343.3 -32681
## - ARI 1 1.0 8343.4 -32681
## - SD 1 1.3 8343.6 -32680
## - CLE 1 1.7 8344.0 -32679
## - CIN 1 1.7 8344.1 -32678
## - DET 1 2.1 8344.5 -32677
## - HOU 1 2.4 8344.7 -32676
## - STL 1 2.4 8344.7 -32676
## - NYG 1 2.8 8345.2 -32675
## - cold_weather 1 3.6 8345.9 -32672
## - DEN 1 5.1 8347.4 -32667
## - forty1 1 9.1 8351.4 -32654
## - avg_rbry_pos 1 26.6 8368.9 -32597
## - avg_rbry_plyr 1 7500.2 15842.6 -15057
##
## Step: AIC=-32684.09
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_fuml_plyr 1 0.0 8342.4 -32686
## - BUF 1 0.0 8342.4 -32686
## - avg_rectd_plyr 1 0.0 8342.4 -32686
## - JAC 1 0.1 8342.4 -32686
## - CHI 1 0.1 8342.4 -32686
## - OAK 1 0.1 8342.4 -32686
## - DAL 1 0.1 8342.4 -32686
## - avg_qbtdp_plyr 1 0.1 8342.4 -32686
## - IND 1 0.1 8342.5 -32686
## - NOR 1 0.1 8342.5 -32686
## - bad_weather_1 1 0.1 8342.5 -32686
## - height 1 0.1 8342.5 -32686
## - MIA 1 0.2 8342.5 -32685
## - NYJ 1 0.2 8342.6 -32685
## - SEA 1 0.2 8342.6 -32685
## - CAR 1 0.3 8342.6 -32685
## - KC 1 0.3 8342.6 -32685
## - grass_1 1 0.3 8342.6 -32685
## - hot_weather 1 0.3 8342.7 -32685
## - TB 1 0.5 8342.8 -32685
## <none> 8342.3 -32684
## - PHI 1 0.6 8343.0 -32684
## - home_team_1 1 0.7 8343.0 -32684
## - TEN 1 0.7 8343.0 -32684
## - ATL 1 0.7 8343.1 -32684
## - NE 1 0.7 8343.1 -32684
## - BAL 1 0.9 8343.2 -32683
## - MINN 1 1.0 8343.3 -32683
## - WAS 1 1.0 8343.3 -32683
## - ARI 1 1.0 8343.4 -32683
## - SD 1 1.3 8343.6 -32682
## - CLE 1 1.7 8344.0 -32680
## - CIN 1 1.8 8344.1 -32680
## - DET 1 2.1 8344.5 -32679
## - STL 1 2.4 8344.8 -32678
## - HOU 1 2.4 8344.8 -32678
## - NYG 1 2.9 8345.2 -32677
## - cold_weather 1 3.6 8345.9 -32674
## - DEN 1 5.1 8347.4 -32669
## - forty1 1 10.8 8353.2 -32650
## - avg_rbry_pos 1 30.3 8372.7 -32586
## - avg_rbry_plyr 1 7517.1 15859.5 -15030
##
## Step: AIC=-32686
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG +
## NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.0 8342.4 -32688
## - avg_rectd_plyr 1 0.0 8342.4 -32688
## - JAC 1 0.1 8342.4 -32688
## - OAK 1 0.1 8342.4 -32688
## - CHI 1 0.1 8342.4 -32688
## - DAL 1 0.1 8342.4 -32688
## - avg_qbtdp_plyr 1 0.1 8342.5 -32688
## - IND 1 0.1 8342.5 -32688
## - NOR 1 0.1 8342.5 -32688
## - bad_weather_1 1 0.1 8342.5 -32688
## - height 1 0.1 8342.5 -32688
## - NYJ 1 0.2 8342.6 -32687
## - MIA 1 0.2 8342.6 -32687
## - SEA 1 0.2 8342.6 -32687
## - CAR 1 0.2 8342.6 -32687
## - KC 1 0.3 8342.6 -32687
## - grass_1 1 0.3 8342.7 -32687
## - hot_weather 1 0.3 8342.7 -32687
## - TB 1 0.5 8342.8 -32686
## <none> 8342.4 -32686
## - PHI 1 0.6 8343.0 -32686
## - home_team_1 1 0.7 8343.0 -32686
## - TEN 1 0.7 8343.0 -32686
## - ATL 1 0.7 8343.1 -32686
## - NE 1 0.7 8343.1 -32686
## - BAL 1 0.9 8343.2 -32685
## - MINN 1 0.9 8343.3 -32685
## - WAS 1 1.0 8343.4 -32685
## - ARI 1 1.1 8343.4 -32685
## - SD 1 1.3 8343.7 -32684
## - CLE 1 1.7 8344.1 -32682
## - CIN 1 1.8 8344.1 -32682
## - DET 1 2.1 8344.5 -32681
## - HOU 1 2.4 8344.8 -32680
## - STL 1 2.4 8344.8 -32680
## - NYG 1 2.9 8345.2 -32679
## - cold_weather 1 3.5 8345.9 -32676
## - DEN 1 5.1 8347.5 -32671
## - forty1 1 10.8 8353.2 -32652
## - avg_rbry_pos 1 30.3 8372.7 -32588
## - avg_rbry_plyr 1 8447.5 16789.9 -13465
##
## Step: AIC=-32687.88
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_rectd_plyr 1 0.0 8342.4 -32690
## - avg_qbtdp_plyr 1 0.1 8342.5 -32690
## - JAC 1 0.1 8342.5 -32690
## - OAK 1 0.1 8342.5 -32690
## - CHI 1 0.1 8342.5 -32690
## - NOR 1 0.1 8342.5 -32690
## - DAL 1 0.1 8342.5 -32690
## - bad_weather_1 1 0.1 8342.5 -32689
## - height 1 0.2 8342.6 -32689
## - IND 1 0.2 8342.6 -32689
## - NYJ 1 0.2 8342.6 -32689
## - SEA 1 0.2 8342.6 -32689
## - CAR 1 0.2 8342.6 -32689
## - KC 1 0.2 8342.6 -32689
## - grass_1 1 0.3 8342.7 -32689
## - MIA 1 0.3 8342.7 -32689
## - hot_weather 1 0.3 8342.7 -32689
## - TB 1 0.6 8343.0 -32688
## - PHI 1 0.6 8343.0 -32688
## <none> 8342.4 -32688
## - home_team_1 1 0.7 8343.1 -32688
## - TEN 1 0.8 8343.2 -32687
## - ATL 1 0.8 8343.2 -32687
## - NE 1 0.9 8343.3 -32687
## - MINN 1 0.9 8343.3 -32687
## - BAL 1 1.0 8343.4 -32686
## - WAS 1 1.1 8343.5 -32686
## - ARI 1 1.2 8343.6 -32686
## - SD 1 1.5 8343.9 -32685
## - CLE 1 2.0 8344.4 -32683
## - CIN 1 2.0 8344.4 -32683
## - DET 1 2.4 8344.8 -32682
## - HOU 1 2.8 8345.2 -32681
## - STL 1 2.8 8345.2 -32681
## - NYG 1 3.2 8345.6 -32679
## - cold_weather 1 3.5 8346.0 -32678
## - DEN 1 5.6 8348.0 -32671
## - forty1 1 10.9 8353.3 -32654
## - avg_rbry_pos 1 30.3 8372.7 -32590
## - avg_rbry_plyr 1 8448.2 16790.6 -13466
##
## Step: AIC=-32689.77
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_qbtdp_plyr 1 0.1 8342.5 -32692
## - JAC 1 0.1 8342.5 -32691
## - OAK 1 0.1 8342.5 -32691
## - CHI 1 0.1 8342.5 -32691
## - NOR 1 0.1 8342.5 -32691
## - DAL 1 0.1 8342.5 -32691
## - bad_weather_1 1 0.1 8342.6 -32691
## - IND 1 0.2 8342.6 -32691
## - NYJ 1 0.2 8342.6 -32691
## - height 1 0.2 8342.6 -32691
## - SEA 1 0.2 8342.6 -32691
## - CAR 1 0.2 8342.6 -32691
## - KC 1 0.2 8342.7 -32691
## - grass_1 1 0.3 8342.7 -32691
## - MIA 1 0.3 8342.7 -32691
## - hot_weather 1 0.3 8342.8 -32691
## - TB 1 0.6 8343.0 -32690
## - PHI 1 0.6 8343.0 -32690
## <none> 8342.4 -32690
## - home_team_1 1 0.7 8343.1 -32690
## - TEN 1 0.8 8343.2 -32689
## - ATL 1 0.8 8343.3 -32689
## - NE 1 0.8 8343.3 -32689
## - MINN 1 0.9 8343.3 -32689
## - BAL 1 1.1 8343.5 -32688
## - WAS 1 1.2 8343.6 -32688
## - ARI 1 1.3 8343.7 -32688
## - SD 1 1.5 8343.9 -32687
## - CLE 1 2.0 8344.4 -32685
## - CIN 1 2.0 8344.5 -32685
## - DET 1 2.4 8344.9 -32684
## - HOU 1 2.8 8345.2 -32683
## - STL 1 2.8 8345.3 -32682
## - NYG 1 3.2 8345.7 -32681
## - cold_weather 1 3.6 8346.0 -32680
## - DEN 1 5.6 8348.1 -32673
## - forty1 1 11.5 8354.0 -32654
## - avg_rbry_pos 1 34.6 8377.0 -32578
## - avg_rbry_plyr 1 8450.6 16793.0 -13464
##
## Step: AIC=-32691.55
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ +
## OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - JAC 1 0.1 8342.6 -32693
## - OAK 1 0.1 8342.6 -32693
## - CHI 1 0.1 8342.6 -32693
## - DAL 1 0.1 8342.6 -32693
## - NOR 1 0.1 8342.6 -32693
## - bad_weather_1 1 0.1 8342.6 -32693
## - IND 1 0.2 8342.7 -32693
## - NYJ 1 0.2 8342.7 -32693
## - SEA 1 0.2 8342.7 -32693
## - height 1 0.2 8342.7 -32693
## - CAR 1 0.2 8342.7 -32693
## - KC 1 0.2 8342.7 -32693
## - grass_1 1 0.3 8342.8 -32693
## - MIA 1 0.3 8342.8 -32693
## - hot_weather 1 0.3 8342.8 -32692
## - PHI 1 0.6 8343.1 -32692
## - TB 1 0.6 8343.1 -32692
## <none> 8342.5 -32692
## - home_team_1 1 0.7 8343.2 -32691
## - TEN 1 0.8 8343.3 -32691
## - ATL 1 0.8 8343.3 -32691
## - NE 1 0.8 8343.3 -32691
## - MINN 1 0.9 8343.4 -32691
## - BAL 1 1.1 8343.6 -32690
## - WAS 1 1.2 8343.7 -32690
## - ARI 1 1.3 8343.8 -32689
## - SD 1 1.5 8344.0 -32689
## - CLE 1 2.0 8344.5 -32687
## - CIN 1 2.0 8344.5 -32687
## - DET 1 2.4 8344.9 -32686
## - HOU 1 2.8 8345.3 -32684
## - STL 1 2.9 8345.4 -32684
## - NYG 1 3.3 8345.8 -32683
## - cold_weather 1 3.6 8346.1 -32682
## - DEN 1 5.6 8348.1 -32675
## - forty1 1 12.9 8355.4 -32651
## - avg_rbry_pos 1 34.6 8377.1 -32580
## - avg_rbry_plyr 1 8496.8 16839.3 -13390
##
## Step: AIC=-32693.25
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK +
## PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.1 8342.7 -32695
## - CHI 1 0.1 8342.7 -32695
## - DAL 1 0.1 8342.7 -32695
## - IND 1 0.1 8342.7 -32695
## - bad_weather_1 1 0.1 8342.7 -32695
## - NOR 1 0.2 8342.8 -32695
## - height 1 0.2 8342.8 -32695
## - NYJ 1 0.2 8342.8 -32695
## - MIA 1 0.2 8342.8 -32694
## - SEA 1 0.2 8342.8 -32694
## - grass_1 1 0.3 8342.9 -32694
## - CAR 1 0.3 8342.9 -32694
## - KC 1 0.3 8342.9 -32694
## - hot_weather 1 0.3 8342.9 -32694
## - TB 1 0.5 8343.1 -32694
## <none> 8342.6 -32693
## - home_team_1 1 0.7 8343.2 -32693
## - PHI 1 0.7 8343.3 -32693
## - TEN 1 0.7 8343.3 -32693
## - ATL 1 0.8 8343.4 -32693
## - NE 1 0.8 8343.4 -32693
## - BAL 1 1.0 8343.6 -32692
## - MINN 1 1.0 8343.6 -32692
## - WAS 1 1.1 8343.7 -32692
## - ARI 1 1.2 8343.8 -32691
## - SD 1 1.4 8344.0 -32691
## - CLE 1 1.9 8344.5 -32689
## - CIN 1 2.0 8344.5 -32689
## - DET 1 2.3 8344.9 -32688
## - HOU 1 2.7 8345.3 -32686
## - STL 1 2.8 8345.4 -32686
## - NYG 1 3.2 8345.8 -32685
## - cold_weather 1 3.5 8346.1 -32684
## - DEN 1 5.5 8348.1 -32677
## - forty1 1 12.9 8355.5 -32653
## - avg_rbry_pos 1 34.6 8377.2 -32581
## - avg_rbry_plyr 1 8497.6 16840.2 -13391
##
## Step: AIC=-32695.01
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET +
## HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI +
## SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - CHI 1 0.1 8342.7 -32697
## - DAL 1 0.1 8342.7 -32697
## - IND 1 0.1 8342.8 -32697
## - bad_weather_1 1 0.1 8342.8 -32697
## - height 1 0.2 8342.9 -32696
## - MIA 1 0.2 8342.9 -32696
## - NOR 1 0.2 8342.9 -32696
## - grass_1 1 0.2 8342.9 -32696
## - NYJ 1 0.3 8342.9 -32696
## - SEA 1 0.3 8343.0 -32696
## - CAR 1 0.3 8343.0 -32696
## - hot_weather 1 0.3 8343.0 -32696
## - KC 1 0.4 8343.0 -32696
## - TB 1 0.5 8343.1 -32695
## <none> 8342.7 -32695
## - home_team_1 1 0.6 8343.3 -32695
## - TEN 1 0.7 8343.3 -32695
## - ATL 1 0.7 8343.4 -32695
## - NE 1 0.7 8343.4 -32695
## - PHI 1 0.8 8343.5 -32694
## - BAL 1 0.9 8343.6 -32694
## - WAS 1 1.0 8343.7 -32694
## - ARI 1 1.1 8343.8 -32693
## - MINN 1 1.1 8343.8 -32693
## - SD 1 1.3 8344.0 -32693
## - CLE 1 1.9 8344.5 -32691
## - CIN 1 1.9 8344.5 -32691
## - DET 1 2.3 8344.9 -32690
## - HOU 1 2.7 8345.3 -32688
## - STL 1 2.7 8345.4 -32688
## - NYG 1 3.1 8345.8 -32687
## - cold_weather 1 3.4 8346.1 -32686
## - DEN 1 5.5 8348.2 -32679
## - forty1 1 12.9 8355.5 -32655
## - avg_rbry_pos 1 35.0 8377.6 -32582
## - avg_rbry_plyr 1 8510.3 16852.9 -13372
##
## Step: AIC=-32696.84
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DAL + DEN + DET + HOU +
## IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD +
## SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DAL 1 0.0 8342.8 -32699
## - IND 1 0.1 8342.8 -32699
## - bad_weather_1 1 0.1 8342.8 -32698
## - MIA 1 0.2 8342.9 -32698
## - height 1 0.2 8342.9 -32698
## - grass_1 1 0.2 8343.0 -32698
## - NOR 1 0.2 8343.0 -32698
## - NYJ 1 0.3 8343.0 -32698
## - SEA 1 0.3 8343.1 -32698
## - hot_weather 1 0.3 8343.1 -32698
## - CAR 1 0.4 8343.1 -32698
## - KC 1 0.4 8343.1 -32698
## - TB 1 0.4 8343.2 -32697
## <none> 8342.7 -32697
## - TEN 1 0.6 8343.4 -32697
## - home_team_1 1 0.6 8343.4 -32697
## - ATL 1 0.7 8343.4 -32697
## - NE 1 0.7 8343.4 -32697
## - PHI 1 0.9 8343.6 -32696
## - BAL 1 0.9 8343.6 -32696
## - WAS 1 1.0 8343.7 -32696
## - ARI 1 1.1 8343.8 -32695
## - MINN 1 1.2 8343.9 -32695
## - SD 1 1.3 8344.0 -32695
## - CLE 1 1.8 8344.5 -32693
## - CIN 1 1.8 8344.6 -32693
## - DET 1 2.2 8344.9 -32692
## - HOU 1 2.6 8345.3 -32690
## - STL 1 2.6 8345.4 -32690
## - NYG 1 3.0 8345.8 -32689
## - cold_weather 1 3.5 8346.2 -32687
## - DEN 1 5.4 8348.2 -32681
## - forty1 1 12.9 8355.6 -32657
## - avg_rbry_pos 1 34.9 8377.6 -32584
## - avg_rbry_plyr 1 8514.0 16856.7 -13368
##
## Step: AIC=-32698.69
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + IND +
## KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA +
## STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - IND 1 0.1 8342.8 -32700
## - bad_weather_1 1 0.1 8342.9 -32700
## - MIA 1 0.2 8342.9 -32700
## - height 1 0.2 8343.0 -32700
## - grass_1 1 0.3 8343.0 -32700
## - NOR 1 0.3 8343.0 -32700
## - hot_weather 1 0.3 8343.1 -32700
## - NYJ 1 0.4 8343.1 -32700
## - SEA 1 0.4 8343.1 -32699
## - TB 1 0.4 8343.2 -32699
## - CAR 1 0.4 8343.2 -32699
## - KC 1 0.4 8343.2 -32699
## <none> 8342.8 -32699
## - TEN 1 0.6 8343.4 -32699
## - home_team_1 1 0.6 8343.4 -32699
## - ATL 1 0.6 8343.4 -32699
## - NE 1 0.6 8343.4 -32699
## - BAL 1 0.8 8343.6 -32698
## - WAS 1 0.9 8343.7 -32698
## - PHI 1 0.9 8343.7 -32698
## - ARI 1 1.0 8343.8 -32697
## - SD 1 1.2 8344.0 -32697
## - MINN 1 1.3 8344.1 -32696
## - CLE 1 1.8 8344.5 -32695
## - CIN 1 1.8 8344.6 -32695
## - DET 1 2.2 8344.9 -32694
## - HOU 1 2.6 8345.3 -32692
## - STL 1 2.6 8345.4 -32692
## - NYG 1 3.0 8345.8 -32691
## - cold_weather 1 3.4 8346.2 -32689
## - DEN 1 5.4 8348.2 -32683
## - forty1 1 12.9 8355.6 -32658
## - avg_rbry_pos 1 34.9 8377.7 -32586
## - avg_rbry_plyr 1 8515.5 16858.3 -13367
##
## Step: AIC=-32700.49
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL +
## TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - bad_weather_1 1 0.1 8342.9 -32702
## - MIA 1 0.1 8343.0 -32702
## - height 1 0.2 8343.0 -32702
## - grass_1 1 0.3 8343.1 -32701
## - NOR 1 0.3 8343.2 -32701
## - hot_weather 1 0.3 8343.2 -32701
## - TB 1 0.4 8343.2 -32701
## - NYJ 1 0.4 8343.2 -32701
## - SEA 1 0.4 8343.3 -32701
## - CAR 1 0.5 8343.3 -32701
## - KC 1 0.5 8343.3 -32701
## - TEN 1 0.6 8343.4 -32701
## - home_team_1 1 0.6 8343.4 -32701
## - ATL 1 0.6 8343.4 -32701
## - NE 1 0.6 8343.4 -32701
## <none> 8342.8 -32700
## - BAL 1 0.8 8343.6 -32700
## - WAS 1 0.9 8343.7 -32700
## - PHI 1 1.0 8343.8 -32699
## - ARI 1 1.0 8343.8 -32699
## - SD 1 1.2 8344.0 -32699
## - MINN 1 1.4 8344.2 -32698
## - CLE 1 1.7 8344.6 -32697
## - CIN 1 1.7 8344.6 -32697
## - DET 1 2.1 8344.9 -32696
## - HOU 1 2.5 8345.3 -32694
## - STL 1 2.5 8345.4 -32694
## - NYG 1 2.9 8345.8 -32693
## - cold_weather 1 3.4 8346.2 -32691
## - DEN 1 5.3 8348.2 -32685
## - forty1 1 12.9 8355.7 -32660
## - avg_rbry_pos 1 34.8 8377.7 -32588
## - avg_rbry_plyr 1 8515.5 16858.3 -13369
##
## Step: AIC=-32702.07
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL +
## TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.1 8343.1 -32704
## - height 1 0.2 8343.1 -32703
## - grass_1 1 0.3 8343.2 -32703
## - NOR 1 0.3 8343.3 -32703
## - hot_weather 1 0.4 8343.3 -32703
## - TB 1 0.4 8343.3 -32703
## - NYJ 1 0.4 8343.3 -32703
## - SEA 1 0.4 8343.4 -32703
## - CAR 1 0.5 8343.4 -32703
## - KC 1 0.5 8343.4 -32702
## - TEN 1 0.6 8343.5 -32702
## - ATL 1 0.6 8343.5 -32702
## - home_team_1 1 0.6 8343.5 -32702
## <none> 8342.9 -32702
## - NE 1 0.6 8343.6 -32702
## - BAL 1 0.8 8343.7 -32701
## - WAS 1 0.9 8343.8 -32701
## - ARI 1 1.0 8343.9 -32701
## - PHI 1 1.0 8344.0 -32701
## - SD 1 1.2 8344.1 -32700
## - MINN 1 1.4 8344.4 -32699
## - CIN 1 1.7 8344.7 -32698
## - CLE 1 1.7 8344.7 -32698
## - DET 1 2.1 8345.1 -32697
## - STL 1 2.5 8345.5 -32696
## - HOU 1 2.5 8345.5 -32696
## - NYG 1 3.0 8345.9 -32694
## - cold_weather 1 3.7 8346.6 -32692
## - DEN 1 5.3 8348.2 -32687
## - forty1 1 12.9 8355.9 -32662
## - avg_rbry_pos 1 34.9 8377.8 -32589
## - avg_rbry_plyr 1 8515.9 16858.8 -13370
##
## Step: AIC=-32703.65
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC +
## MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB +
## TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
##
## Df Sum of Sq RSS AIC
## - height 1 0.2 8343.3 -32705
## - grass_1 1 0.3 8343.4 -32705
## - TB 1 0.3 8343.4 -32705
## - hot_weather 1 0.4 8343.4 -32704
## - NOR 1 0.4 8343.5 -32704
## - NYJ 1 0.4 8343.5 -32704
## - SEA 1 0.5 8343.6 -32704
## - TEN 1 0.5 8343.6 -32704
## - CAR 1 0.5 8343.6 -32704
## - ATL 1 0.5 8343.6 -32704
## - KC 1 0.5 8343.6 -32704
## - NE 1 0.6 8343.6 -32704
## <none> 8343.1 -32704
## - home_team_1 1 0.6 8343.7 -32704
## - BAL 1 0.7 8343.8 -32703
## - WAS 1 0.8 8343.9 -32703
## - ARI 1 0.9 8344.0 -32703
## - PHI 1 1.1 8344.2 -32702
## - SD 1 1.1 8344.2 -32702
## - MINN 1 1.5 8344.6 -32701
## - CIN 1 1.7 8344.7 -32700
## - CLE 1 1.7 8344.8 -32700
## - DET 1 2.0 8345.1 -32699
## - STL 1 2.4 8345.5 -32698
## - HOU 1 2.4 8345.5 -32698
## - NYG 1 2.9 8345.9 -32696
## - cold_weather 1 3.6 8346.7 -32694
## - DEN 1 5.2 8348.3 -32689
## - forty1 1 13.0 8356.0 -32663
## - avg_rbry_pos 1 34.9 8378.0 -32591
## - avg_rbry_plyr 1 8517.7 16860.7 -13369
##
## Step: AIC=-32705
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN +
## WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 0.3 8343.6 -32706
## - TB 1 0.3 8343.6 -32706
## - hot_weather 1 0.4 8343.6 -32706
## - NOR 1 0.4 8343.6 -32706
## - NYJ 1 0.4 8343.7 -32706
## - SEA 1 0.5 8343.7 -32705
## - TEN 1 0.5 8343.8 -32705
## - CAR 1 0.5 8343.8 -32705
## - KC 1 0.5 8343.8 -32705
## - ATL 1 0.6 8343.8 -32705
## <none> 8343.3 -32705
## - home_team_1 1 0.6 8343.9 -32705
## - NE 1 0.6 8343.9 -32705
## - BAL 1 0.7 8344.0 -32705
## - WAS 1 0.9 8344.1 -32704
## - ARI 1 0.9 8344.2 -32704
## - PHI 1 1.1 8344.3 -32704
## - SD 1 1.1 8344.4 -32703
## - MINN 1 1.5 8344.8 -32702
## - CIN 1 1.7 8345.0 -32701
## - CLE 1 1.7 8345.0 -32701
## - DET 1 2.0 8345.3 -32700
## - HOU 1 2.4 8345.7 -32699
## - STL 1 2.5 8345.7 -32699
## - NYG 1 2.9 8346.1 -32698
## - cold_weather 1 3.6 8346.9 -32695
## - DEN 1 5.2 8348.5 -32690
## - forty1 1 15.4 8358.7 -32656
## - avg_rbry_pos 1 45.2 8388.4 -32559
## - avg_rbry_plyr 1 8556.5 16899.8 -13307
##
## Step: AIC=-32706.08
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN +
## WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - NOR 1 0.3 8343.9 -32707
## - TB 1 0.3 8343.9 -32707
## - NYJ 1 0.4 8343.9 -32707
## - SEA 1 0.4 8343.9 -32707
## - hot_weather 1 0.4 8344.0 -32707
## - TEN 1 0.5 8344.0 -32707
## - home_team_1 1 0.5 8344.0 -32706
## - CAR 1 0.6 8344.1 -32706
## - KC 1 0.6 8344.2 -32706
## <none> 8343.6 -32706
## - ATL 1 0.6 8344.2 -32706
## - NE 1 0.8 8344.3 -32706
## - BAL 1 0.8 8344.4 -32705
## - WAS 1 0.8 8344.4 -32705
## - ARI 1 1.0 8344.5 -32705
## - SD 1 1.0 8344.6 -32705
## - PHI 1 1.1 8344.7 -32704
## - MINN 1 1.4 8345.0 -32703
## - CLE 1 1.6 8345.2 -32703
## - CIN 1 1.9 8345.4 -32702
## - DET 1 2.2 8345.7 -32701
## - HOU 1 2.6 8346.1 -32700
## - STL 1 2.6 8346.2 -32699
## - NYG 1 3.1 8346.7 -32698
## - cold_weather 1 3.5 8347.1 -32696
## - DEN 1 5.1 8348.7 -32691
## - forty1 1 15.4 8359.0 -32657
## - avg_rbry_pos 1 45.1 8388.7 -32560
## - avg_rbry_plyr 1 8556.7 16900.2 -13309
##
## Step: AIC=-32707.06
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + WAS +
## avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - NYJ 1 0.3 8344.2 -32708
## - SEA 1 0.3 8344.2 -32708
## - TB 1 0.4 8344.2 -32708
## - hot_weather 1 0.4 8344.3 -32708
## - CAR 1 0.5 8344.4 -32707
## - KC 1 0.5 8344.4 -32707
## - home_team_1 1 0.5 8344.4 -32707
## - TEN 1 0.6 8344.4 -32707
## <none> 8343.9 -32707
## - ATL 1 0.7 8344.6 -32707
## - NE 1 0.9 8344.7 -32706
## - BAL 1 0.9 8344.8 -32706
## - WAS 1 0.9 8344.8 -32706
## - PHI 1 1.0 8344.9 -32706
## - ARI 1 1.1 8345.0 -32705
## - SD 1 1.2 8345.0 -32705
## - MINN 1 1.3 8345.2 -32705
## - CLE 1 1.8 8345.6 -32703
## - CIN 1 2.0 8345.9 -32702
## - DET 1 2.4 8346.3 -32701
## - HOU 1 2.8 8346.6 -32700
## - STL 1 2.8 8346.7 -32700
## - NYG 1 3.3 8347.2 -32698
## - cold_weather 1 3.6 8347.5 -32697
## - DEN 1 5.4 8349.2 -32691
## - forty1 1 15.5 8359.3 -32658
## - avg_rbry_pos 1 44.9 8388.8 -32561
## - avg_rbry_plyr 1 8570.1 16914.0 -13289
##
## Step: AIC=-32708.07
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NYG + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.3 8344.4 -32709
## - CAR 1 0.4 8344.6 -32709
## - TB 1 0.4 8344.6 -32709
## - hot_weather 1 0.4 8344.6 -32709
## - KC 1 0.5 8344.6 -32709
## - home_team_1 1 0.5 8344.7 -32708
## <none> 8344.2 -32708
## - TEN 1 0.6 8344.8 -32708
## - ATL 1 0.8 8345.0 -32707
## - PHI 1 0.9 8345.1 -32707
## - NE 1 1.0 8345.1 -32707
## - BAL 1 1.0 8345.2 -32707
## - WAS 1 1.0 8345.2 -32707
## - MINN 1 1.2 8345.4 -32706
## - ARI 1 1.2 8345.4 -32706
## - SD 1 1.3 8345.4 -32706
## - CLE 1 1.9 8346.1 -32704
## - CIN 1 2.2 8346.4 -32703
## - DET 1 2.5 8346.7 -32702
## - HOU 1 2.9 8347.1 -32700
## - STL 1 3.0 8347.2 -32700
## - NYG 1 3.5 8347.7 -32698
## - cold_weather 1 3.6 8347.7 -32698
## - DEN 1 5.7 8349.8 -32691
## - forty1 1 15.5 8359.6 -32659
## - avg_rbry_pos 1 45.1 8389.2 -32562
## - avg_rbry_plyr 1 8572.8 16917.0 -13286
##
## Step: AIC=-32709.21
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN +
## NE + NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - CAR 1 0.4 8344.8 -32710
## - KC 1 0.4 8344.8 -32710
## - hot_weather 1 0.5 8344.9 -32710
## - TB 1 0.5 8344.9 -32710
## - home_team_1 1 0.5 8344.9 -32710
## <none> 8344.4 -32709
## - TEN 1 0.7 8345.1 -32709
## - PHI 1 0.9 8345.3 -32708
## - ATL 1 0.9 8345.3 -32708
## - NE 1 1.1 8345.5 -32708
## - BAL 1 1.1 8345.5 -32708
## - WAS 1 1.1 8345.6 -32707
## - MINN 1 1.1 8345.6 -32707
## - ARI 1 1.3 8345.7 -32707
## - SD 1 1.4 8345.8 -32707
## - CLE 1 2.0 8346.5 -32705
## - CIN 1 2.3 8346.8 -32704
## - DET 1 2.7 8347.1 -32702
## - HOU 1 3.1 8347.5 -32701
## - STL 1 3.1 8347.6 -32701
## - cold_weather 1 3.5 8347.9 -32700
## - NYG 1 3.7 8348.2 -32699
## - DEN 1 5.9 8350.3 -32692
## - forty1 1 15.6 8360.0 -32660
## - avg_rbry_pos 1 45.2 8389.6 -32563
## - avg_rbry_plyr 1 8574.3 16918.7 -13285
##
## Step: AIC=-32709.96
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CIN + CLE + DEN + DET + HOU + KC + MINN + NE +
## NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - KC 1 0.4 8345.2 -32711
## - hot_weather 1 0.5 8345.3 -32710
## - home_team_1 1 0.5 8345.3 -32710
## - TB 1 0.6 8345.4 -32710
## <none> 8344.8 -32710
## - TEN 1 0.8 8345.6 -32709
## - PHI 1 0.8 8345.6 -32709
## - ATL 1 1.0 8345.8 -32709
## - MINN 1 1.1 8345.9 -32708
## - NE 1 1.2 8346.0 -32708
## - BAL 1 1.2 8346.0 -32708
## - WAS 1 1.2 8346.0 -32708
## - ARI 1 1.4 8346.2 -32707
## - SD 1 1.5 8346.3 -32707
## - CLE 1 2.2 8347.0 -32705
## - CIN 1 2.5 8347.3 -32704
## - DET 1 2.8 8347.6 -32703
## - HOU 1 3.2 8348.0 -32701
## - STL 1 3.3 8348.1 -32701
## - cold_weather 1 3.5 8348.3 -32700
## - NYG 1 3.9 8348.7 -32699
## - DEN 1 6.2 8351.0 -32692
## - forty1 1 15.6 8360.4 -32661
## - avg_rbry_pos 1 45.4 8390.2 -32563
## - avg_rbry_plyr 1 8575.7 16920.5 -13284
##
## Step: AIC=-32710.78
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI +
## ATL + BAL + CIN + CLE + DEN + DET + HOU + MINN + NE + NYG +
## PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.4 8345.6 -32711
## - home_team_1 1 0.4 8345.6 -32711
## <none> 8345.2 -32711
## - TB 1 0.6 8345.8 -32711
## - PHI 1 0.7 8345.9 -32710
## - TEN 1 0.9 8346.0 -32710
## - MINN 1 1.0 8346.1 -32710
## - ATL 1 1.1 8346.2 -32709
## - NE 1 1.3 8346.4 -32709
## - BAL 1 1.3 8346.5 -32709
## - WAS 1 1.3 8346.5 -32708
## - ARI 1 1.5 8346.7 -32708
## - SD 1 1.6 8346.7 -32708
## - CLE 1 2.3 8347.5 -32705
## - CIN 1 2.6 8347.8 -32704
## - DET 1 2.9 8348.1 -32703
## - HOU 1 3.4 8348.5 -32702
## - STL 1 3.4 8348.6 -32701
## - cold_weather 1 3.5 8348.6 -32701
## - NYG 1 4.1 8349.3 -32699
## - DEN 1 6.4 8351.6 -32692
## - forty1 1 15.6 8360.8 -32661
## - avg_rbry_pos 1 45.3 8390.5 -32564
## - avg_rbry_plyr 1 8575.8 16921.0 -13285
##
## Step: AIC=-32711.31
## ra ~ cold_weather + home_team_1 + forty1 + ARI + ATL + BAL +
## CIN + CLE + DEN + DET + HOU + MINN + NE + NYG + PHI + SD +
## STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## - home_team_1 1 0.4 8346.0 -32712
## - TB 1 0.6 8346.2 -32711
## <none> 8345.6 -32711
## - PHI 1 0.7 8346.3 -32711
## - TEN 1 0.9 8346.5 -32710
## - MINN 1 1.0 8346.6 -32710
## - ATL 1 1.1 8346.7 -32710
## - NE 1 1.3 8346.9 -32709
## - BAL 1 1.3 8346.9 -32709
## - WAS 1 1.3 8347.0 -32709
## - SD 1 1.5 8347.1 -32708
## - ARI 1 1.5 8347.1 -32708
## - CLE 1 2.3 8347.9 -32706
## - CIN 1 2.6 8348.2 -32705
## - DET 1 3.0 8348.6 -32704
## - STL 1 3.4 8349.0 -32702
## - HOU 1 3.4 8349.0 -32702
## - cold_weather 1 3.5 8349.1 -32702
## - NYG 1 4.1 8349.7 -32700
## - DEN 1 6.4 8352.0 -32692
## - forty1 1 15.7 8361.3 -32662
## - avg_rbry_pos 1 45.4 8391.0 -32564
## - avg_rbry_plyr 1 8575.4 16921.0 -13287
##
## Step: AIC=-32711.86
## ra ~ cold_weather + forty1 + ARI + ATL + BAL + CIN + CLE + DEN +
## DET + HOU + MINN + NE + NYG + PHI + SD + STL + TB + TEN +
## WAS + avg_rbry_plyr + avg_rbry_pos
##
## Df Sum of Sq RSS AIC
## <none> 8346.0 -32712
## - TB 1 0.6 8346.7 -32712
## - PHI 1 0.7 8346.7 -32712
## - TEN 1 0.9 8347.0 -32711
## - ATL 1 0.9 8347.0 -32711
## - MINN 1 1.0 8347.0 -32711
## - NE 1 1.3 8347.4 -32709
## - ARI 1 1.3 8347.4 -32709
## - BAL 1 1.3 8347.4 -32709
## - WAS 1 1.4 8347.5 -32709
## - SD 1 1.5 8347.6 -32709
## - CLE 1 2.4 8348.4 -32706
## - CIN 1 2.7 8348.7 -32705
## - DET 1 2.8 8348.8 -32705
## - STL 1 3.2 8349.2 -32703
## - HOU 1 3.2 8349.2 -32703
## - cold_weather 1 3.8 8349.8 -32701
## - NYG 1 4.2 8350.2 -32700
## - DEN 1 6.5 8352.6 -32692
## - forty1 1 15.6 8361.7 -32662
## - avg_rbry_pos 1 45.4 8391.4 -32565
## - avg_rbry_plyr 1 8575.6 16921.6 -13288Fumbles
PreProcess:
set.seed(123)
splitfuml <- sample.split(nfl_data$fuml, SplitRatio = 0.7)
Trainfuml <- subset(nfl_data, split == TRUE)
Testfuml <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainfuml, method = c("center", "scale"))
trainTransformedfuml <- predict(preProcValues, Trainfuml)
testTransformedfuml <- predict(preProcValues, Testfuml)ggpairs:
ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[1:9]))])
ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[10:18]))])
ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[19:27]))])
ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[28:36]))])
ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[37:45]))])
ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[46:51]))])
fumlregform <- formula(paste("fuml ~ ",
paste(colnames(filtered_nfl_data_fields), collapse="+")))
linRegFumble <- lm(fumlregform, data = trainTransformedfuml)
summary(linRegFumble)##
## Call:
## lm(formula = fumlregform, data = trainTransformedfuml)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.2702 -0.2647 -0.1117 -0.0102 15.9907
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.587e-16 5.750e-03 0.000 1.0000
## height 4.911e-03 1.116e-02 0.440 0.6598
## weight 6.203e-04 1.046e-02 0.059 0.9527
## cold_weather 1.146e-02 6.053e-03 1.893 0.0583 .
## hot_weather 8.272e-04 5.803e-03 0.143 0.8866
## home_team_1 -3.380e-03 6.257e-03 -0.540 0.5890
## forty1 -4.425e-03 9.924e-03 -0.446 0.6556
## vertical1 -4.639e-03 7.630e-03 -0.608 0.5432
## ARI -5.726e-03 8.044e-03 -0.712 0.4766
## ATL -3.851e-03 8.082e-03 -0.477 0.6337
## BAL -6.381e-03 8.089e-03 -0.789 0.4302
## BUF -4.508e-03 7.985e-03 -0.565 0.5724
## CAR -5.196e-03 7.933e-03 -0.655 0.5125
## CHI -1.287e-02 7.844e-03 -1.641 0.1009
## CIN -8.660e-03 7.989e-03 -1.084 0.2784
## CLE -3.170e-03 7.952e-03 -0.399 0.6902
## DAL -4.528e-03 8.033e-03 -0.564 0.5730
## DEN -1.587e-03 8.063e-03 -0.197 0.8440
## DET -3.160e-03 7.952e-03 -0.397 0.6911
## GB -3.152e-03 8.187e-03 -0.385 0.7002
## HOU -1.501e-03 8.089e-03 -0.186 0.8528
## IND -1.066e-02 8.030e-03 -1.328 0.1843
## JAC -2.399e-03 7.833e-03 -0.306 0.7595
## KC -7.052e-04 8.005e-03 -0.088 0.9298
## MIA -2.711e-04 7.876e-03 -0.034 0.9725
## MINN -3.456e-03 7.924e-03 -0.436 0.6628
## NE -1.030e-02 8.276e-03 -1.244 0.2134
## NOR -1.055e-02 8.251e-03 -1.279 0.2008
## NYG 1.798e-03 8.064e-03 0.223 0.8236
## NYJ -1.242e-02 8.035e-03 -1.546 0.1220
## OAK -6.913e-04 8.085e-03 -0.085 0.9319
## PHI 1.705e-03 7.835e-03 0.218 0.8278
## PIT -5.273e-03 8.040e-03 -0.656 0.5119
## SD -9.969e-04 7.890e-03 -0.126 0.8995
## SEA 9.747e-04 8.189e-03 0.119 0.9053
## STL -9.614e-04 7.970e-03 -0.121 0.9040
## TB -3.135e-03 7.895e-03 -0.397 0.6913
## TEN -7.993e-03 7.943e-03 -1.006 0.3143
## WAS -4.065e-03 7.985e-03 -0.509 0.6107
## avg_trg_team NA NA NA NA
## avg_rectd_plyr -2.112e-03 7.343e-03 -0.288 0.7736
## avg_tdr_team NA NA NA NA
## avg_rbra_team NA NA NA NA
## avg_rbry_plyr -4.601e-03 8.787e-03 -0.524 0.6006
## avg_rbry_pos 5.521e-03 1.024e-02 0.539 0.5898
## avg_fuml_plyr 3.088e-01 8.494e-03 36.352 <2e-16 ***
## avg_fuml_team NA NA NA NA
## avg_qbints_team NA NA NA NA
## avg_qbtdp_plyr -8.624e-03 9.227e-03 -0.935 0.3499
## avg_qbtdp_team NA NA NA NA
## grass_1 -8.645e-03 6.616e-03 -1.307 0.1913
## bad_weather_1 1.779e-03 5.850e-03 0.304 0.7610
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9533 on 27438 degrees of freedom
## Multiple R-squared: 0.09271, Adjusted R-squared: 0.09122
## F-statistic: 62.31 on 45 and 27438 DF, p-value: < 2.2e-16linRegFumble2 <- lm(fuml ~ avg_fuml_plyr, data = trainTransformedfuml)
summary(linRegFumble2)##
## Call:
## lm(formula = fuml ~ avg_fuml_plyr, data = trainTransformedfuml)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.2292 -0.2679 -0.1108 0.0000 16.0207
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.991e-16 5.748e-03 0.00 1
## avg_fuml_plyr 3.033e-01 5.748e-03 52.76 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9529 on 27482 degrees of freedom
## Multiple R-squared: 0.09197, Adjusted R-squared: 0.09194
## F-statistic: 2784 on 1 and 27482 DF, p-value: < 2.2e-16Definitely does not seem to be a good predictor
Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing
FumblePredicted <- predict(linRegFumble2, newdata = testTransformedfuml)
SSEfum <- sum((FumblePredicted - testTransformedfuml$fuml)^2)
SSTfum <- sum((mean(nfl_data$fuml)-testTransformedfuml$fuml)^2)
r2_fum <- 1 - SSEfum/SSTfum
r2_fum## [1] 0.08604778rmse_fum <- sqrt(SSEfum/nrow(testTransformedfuml))
rmse_fum## [1] 0.9529244Regression plots:
par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegFumble2, which = c(1:3,5))
The plots don’t seem to confirm that this is a good model for the data
Summary statistics:
confint(linRegFumble2)## 2.5 % 97.5 %
## (Intercept) -0.01126638 0.01126638
## avg_fuml_plyr 0.29200585 0.31453901coef(summary(linRegFumble2))## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.990785e-16 0.005748004 3.463437e-14 1
## avg_fuml_plyr 3.032724e-01 0.005748108 5.276039e+01 0anova(linRegFumble2)## Analysis of Variance Table
##
## Response: fuml
## Df Sum Sq Mean Sq F value Pr(>F)
## avg_fuml_plyr 1 2527.7 2527.73 2783.7 < 2.2e-16 ***
## Residuals 27482 24955.3 0.91
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AIC:
aic_fuml <- step(lm(fumlregform, data = trainTransformedfuml), direction = "backward")## Start: AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## avg_qbtdp_team + grass_1 + bad_weather_1
##
##
## Step: AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
##
## Step: AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
##
## Step: AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
##
## Step: AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD +
## SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - MIA 1 0.00 24935 -2585.0
## - weight 1 0.00 24935 -2585.0
## - OAK 1 0.01 24935 -2585.0
## - KC 1 0.01 24935 -2585.0
## - SEA 1 0.01 24935 -2585.0
## - STL 1 0.01 24935 -2585.0
## - SD 1 0.01 24935 -2585.0
## - hot_weather 1 0.02 24935 -2585.0
## - HOU 1 0.03 24935 -2585.0
## - DEN 1 0.04 24935 -2585.0
## - PHI 1 0.04 24935 -2585.0
## - NYG 1 0.05 24935 -2585.0
## - avg_rectd_plyr 1 0.08 24935 -2585.0
## - bad_weather_1 1 0.08 24935 -2584.9
## - JAC 1 0.09 24935 -2584.9
## - GB 1 0.13 24935 -2584.9
## - TB 1 0.14 24935 -2584.9
## - DET 1 0.14 24935 -2584.9
## - CLE 1 0.14 24935 -2584.9
## - MINN 1 0.17 24935 -2584.8
## - height 1 0.18 24935 -2584.8
## - forty1 1 0.18 24935 -2584.8
## - ATL 1 0.21 24935 -2584.8
## - WAS 1 0.24 24935 -2584.8
## - avg_rbry_plyr 1 0.25 24935 -2584.8
## - avg_rbry_pos 1 0.26 24935 -2584.8
## - home_team_1 1 0.27 24935 -2584.8
## - DAL 1 0.29 24935 -2584.7
## - BUF 1 0.29 24935 -2584.7
## - vertical1 1 0.34 24935 -2584.7
## - CAR 1 0.39 24935 -2584.6
## - PIT 1 0.39 24935 -2584.6
## - ARI 1 0.46 24936 -2584.5
## - BAL 1 0.57 24936 -2584.4
## - avg_qbtdp_plyr 1 0.79 24936 -2584.2
## - TEN 1 0.92 24936 -2584.0
## - CIN 1 1.07 24936 -2583.9
## - NE 1 1.41 24936 -2583.5
## - NOR 1 1.49 24937 -2583.4
## - grass_1 1 1.55 24937 -2583.3
## - IND 1 1.60 24937 -2583.3
## <none> 24935 -2583.0
## - NYJ 1 2.17 24937 -2582.6
## - CHI 1 2.45 24938 -2582.3
## - cold_weather 1 3.26 24938 -2581.4
## - avg_fuml_plyr 1 1200.94 26136 -1292.2
##
## Step: AIC=-2585.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 +
## forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI +
## CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC +
## MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA +
## STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - weight 1 0.00 24935 -2587.0
## - OAK 1 0.01 24935 -2587.0
## - KC 1 0.01 24935 -2587.0
## - STL 1 0.01 24935 -2587.0
## - SD 1 0.01 24935 -2587.0
## - hot_weather 1 0.02 24935 -2587.0
## - SEA 1 0.02 24935 -2587.0
## - HOU 1 0.03 24935 -2587.0
## - DEN 1 0.04 24935 -2587.0
## - PHI 1 0.06 24935 -2587.0
## - NYG 1 0.07 24935 -2587.0
## - avg_rectd_plyr 1 0.08 24935 -2587.0
## - bad_weather_1 1 0.08 24935 -2586.9
## - JAC 1 0.10 24935 -2586.9
## - GB 1 0.16 24935 -2586.9
## - DET 1 0.17 24935 -2586.8
## - TB 1 0.17 24935 -2586.8
## - CLE 1 0.17 24935 -2586.8
## - height 1 0.18 24935 -2586.8
## - forty1 1 0.18 24935 -2586.8
## - MINN 1 0.21 24935 -2586.8
## - avg_rbry_plyr 1 0.25 24935 -2586.8
## - ATL 1 0.25 24935 -2586.8
## - avg_rbry_pos 1 0.26 24935 -2586.8
## - home_team_1 1 0.27 24935 -2586.8
## - WAS 1 0.29 24935 -2586.7
## - vertical1 1 0.33 24935 -2586.7
## - DAL 1 0.35 24935 -2586.7
## - BUF 1 0.35 24935 -2586.7
## - CAR 1 0.48 24936 -2586.5
## - PIT 1 0.49 24936 -2586.5
## - ARI 1 0.57 24936 -2586.4
## - BAL 1 0.71 24936 -2586.2
## - avg_qbtdp_plyr 1 0.79 24936 -2586.2
## - TEN 1 1.16 24936 -2585.8
## - CIN 1 1.35 24936 -2585.6
## - grass_1 1 1.55 24937 -2585.3
## - NE 1 1.79 24937 -2585.1
## <none> 24935 -2585.0
## - NOR 1 1.91 24937 -2584.9
## - IND 1 2.03 24937 -2584.8
## - NYJ 1 2.77 24938 -2584.0
## - CHI 1 3.11 24938 -2583.6
## - cold_weather 1 3.26 24938 -2583.4
## - avg_fuml_plyr 1 1201.25 26136 -1293.9
##
## Step: AIC=-2587.03
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MINN + NE +
## NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB +
## TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - OAK 1 0.01 24935 -2589.0
## - KC 1 0.01 24935 -2589.0
## - STL 1 0.01 24935 -2589.0
## - SD 1 0.01 24935 -2589.0
## - hot_weather 1 0.02 24935 -2589.0
## - SEA 1 0.02 24935 -2589.0
## - HOU 1 0.03 24935 -2589.0
## - DEN 1 0.04 24935 -2589.0
## - PHI 1 0.06 24935 -2589.0
## - NYG 1 0.07 24935 -2589.0
## - avg_rectd_plyr 1 0.07 24935 -2588.9
## - bad_weather_1 1 0.08 24935 -2588.9
## - JAC 1 0.10 24935 -2588.9
## - GB 1 0.16 24935 -2588.9
## - DET 1 0.17 24935 -2588.8
## - TB 1 0.17 24935 -2588.8
## - CLE 1 0.17 24935 -2588.8
## - forty1 1 0.19 24935 -2588.8
## - MINN 1 0.21 24935 -2588.8
## - avg_rbry_plyr 1 0.25 24935 -2588.8
## - ATL 1 0.25 24935 -2588.8
## - home_team_1 1 0.27 24935 -2588.7
## - WAS 1 0.29 24935 -2588.7
## - vertical1 1 0.33 24935 -2588.7
## - avg_rbry_pos 1 0.33 24935 -2588.7
## - DAL 1 0.35 24935 -2588.6
## - BUF 1 0.36 24935 -2588.6
## - height 1 0.43 24936 -2588.6
## - CAR 1 0.48 24936 -2588.5
## - PIT 1 0.49 24936 -2588.5
## - ARI 1 0.57 24936 -2588.4
## - BAL 1 0.71 24936 -2588.2
## - avg_qbtdp_plyr 1 0.88 24936 -2588.1
## - TEN 1 1.17 24936 -2587.8
## - CIN 1 1.36 24936 -2587.5
## - grass_1 1 1.55 24937 -2587.3
## - NE 1 1.80 24937 -2587.1
## <none> 24935 -2587.0
## - NOR 1 1.91 24937 -2586.9
## - IND 1 2.03 24937 -2586.8
## - NYJ 1 2.77 24938 -2586.0
## - CHI 1 3.12 24938 -2585.6
## - cold_weather 1 3.26 24938 -2585.4
## - avg_fuml_plyr 1 1211.40 26146 -1285.2
##
## Step: AIC=-2589.03
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + KC + MINN + NE +
## NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TB + TEN +
## WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - KC 1 0.00 24935 -2591.0
## - STL 1 0.01 24935 -2591.0
## - SD 1 0.01 24935 -2591.0
## - hot_weather 1 0.02 24935 -2591.0
## - HOU 1 0.03 24935 -2591.0
## - DEN 1 0.03 24935 -2591.0
## - SEA 1 0.03 24935 -2591.0
## - avg_rectd_plyr 1 0.07 24935 -2590.9
## - bad_weather_1 1 0.08 24935 -2590.9
## - PHI 1 0.09 24935 -2590.9
## - NYG 1 0.09 24935 -2590.9
## - JAC 1 0.09 24935 -2590.9
## - GB 1 0.16 24935 -2590.8
## - DET 1 0.17 24935 -2590.8
## - TB 1 0.17 24935 -2590.8
## - CLE 1 0.17 24935 -2590.8
## - forty1 1 0.19 24935 -2590.8
## - MINN 1 0.21 24935 -2590.8
## - avg_rbry_plyr 1 0.24 24935 -2590.8
## - ATL 1 0.25 24935 -2590.8
## - home_team_1 1 0.26 24935 -2590.7
## - WAS 1 0.29 24935 -2590.7
## - avg_rbry_pos 1 0.33 24935 -2590.7
## - vertical1 1 0.33 24935 -2590.7
## - DAL 1 0.36 24935 -2590.6
## - BUF 1 0.37 24935 -2590.6
## - height 1 0.42 24936 -2590.6
## - CAR 1 0.50 24936 -2590.5
## - PIT 1 0.51 24936 -2590.5
## - ARI 1 0.60 24936 -2590.4
## - BAL 1 0.76 24936 -2590.2
## - avg_qbtdp_plyr 1 0.88 24936 -2590.1
## - TEN 1 1.26 24936 -2589.6
## - CIN 1 1.45 24937 -2589.4
## - grass_1 1 1.56 24937 -2589.3
## <none> 24935 -2589.0
## - NE 1 1.93 24937 -2588.9
## - NOR 1 2.08 24937 -2588.7
## - IND 1 2.19 24937 -2588.6
## - NYJ 1 3.01 24938 -2587.7
## - cold_weather 1 3.26 24938 -2587.4
## - CHI 1 3.40 24938 -2587.3
## - avg_fuml_plyr 1 1211.79 26147 -1286.8
##
## Step: AIC=-2591.02
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR +
## NYG + NYJ + PHI + PIT + SD + SEA + STL + TB + TEN + WAS +
## avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - STL 1 0.01 24935 -2593.0
## - SD 1 0.01 24935 -2593.0
## - hot_weather 1 0.02 24935 -2593.0
## - HOU 1 0.03 24935 -2593.0
## - DEN 1 0.03 24935 -2593.0
## - SEA 1 0.04 24935 -2593.0
## - avg_rectd_plyr 1 0.07 24935 -2592.9
## - bad_weather_1 1 0.08 24935 -2592.9
## - JAC 1 0.09 24935 -2592.9
## - PHI 1 0.10 24935 -2592.9
## - NYG 1 0.11 24935 -2592.9
## - GB 1 0.16 24935 -2592.8
## - DET 1 0.17 24935 -2592.8
## - TB 1 0.17 24935 -2592.8
## - CLE 1 0.17 24935 -2592.8
## - forty1 1 0.19 24935 -2592.8
## - MINN 1 0.21 24935 -2592.8
## - avg_rbry_plyr 1 0.24 24935 -2592.8
## - ATL 1 0.25 24935 -2592.7
## - home_team_1 1 0.26 24935 -2592.7
## - WAS 1 0.30 24935 -2592.7
## - vertical1 1 0.33 24935 -2592.7
## - avg_rbry_pos 1 0.33 24935 -2592.7
## - DAL 1 0.37 24935 -2592.6
## - BUF 1 0.37 24935 -2592.6
## - height 1 0.43 24936 -2592.6
## - CAR 1 0.52 24936 -2592.5
## - PIT 1 0.53 24936 -2592.4
## - ARI 1 0.62 24936 -2592.3
## - BAL 1 0.78 24936 -2592.2
## - avg_qbtdp_plyr 1 0.88 24936 -2592.1
## - TEN 1 1.31 24936 -2591.6
## - CIN 1 1.51 24937 -2591.4
## - grass_1 1 1.57 24937 -2591.3
## <none> 24935 -2591.0
## - NE 1 2.02 24937 -2590.8
## - NOR 1 2.17 24937 -2590.6
## - IND 1 2.28 24937 -2590.5
## - NYJ 1 3.15 24938 -2589.6
## - cold_weather 1 3.26 24938 -2589.4
## - CHI 1 3.57 24939 -2589.1
## - avg_fuml_plyr 1 1211.80 26147 -1288.8
##
## Step: AIC=-2593.02
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR +
## NYG + NYJ + PHI + PIT + SD + SEA + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - SD 1 0.01 24935 -2595.0
## - hot_weather 1 0.02 24935 -2595.0
## - HOU 1 0.02 24935 -2595.0
## - DEN 1 0.03 24935 -2595.0
## - SEA 1 0.05 24935 -2595.0
## - avg_rectd_plyr 1 0.07 24935 -2594.9
## - JAC 1 0.08 24935 -2594.9
## - bad_weather_1 1 0.09 24935 -2594.9
## - PHI 1 0.12 24935 -2594.9
## - NYG 1 0.12 24935 -2594.9
## - GB 1 0.15 24935 -2594.8
## - DET 1 0.16 24935 -2594.8
## - TB 1 0.16 24935 -2594.8
## - CLE 1 0.16 24935 -2594.8
## - forty1 1 0.19 24935 -2594.8
## - MINN 1 0.20 24935 -2594.8
## - avg_rbry_plyr 1 0.24 24935 -2594.8
## - ATL 1 0.25 24935 -2594.7
## - home_team_1 1 0.26 24935 -2594.7
## - WAS 1 0.29 24935 -2594.7
## - vertical1 1 0.33 24935 -2594.7
## - avg_rbry_pos 1 0.33 24935 -2594.7
## - DAL 1 0.36 24935 -2594.6
## - BUF 1 0.37 24935 -2594.6
## - height 1 0.43 24936 -2594.5
## - CAR 1 0.51 24936 -2594.4
## - PIT 1 0.52 24936 -2594.4
## - ARI 1 0.62 24936 -2594.3
## - BAL 1 0.78 24936 -2594.2
## - avg_qbtdp_plyr 1 0.88 24936 -2594.1
## - TEN 1 1.32 24936 -2593.6
## - CIN 1 1.53 24937 -2593.3
## - grass_1 1 1.57 24937 -2593.3
## <none> 24935 -2593.0
## - NE 1 2.06 24937 -2592.8
## - NOR 1 2.23 24937 -2592.6
## - IND 1 2.34 24937 -2592.4
## - NYJ 1 3.23 24938 -2591.4
## - cold_weather 1 3.26 24938 -2591.4
## - CHI 1 3.63 24939 -2591.0
## - avg_fuml_plyr 1 1212.23 26147 -1290.3
##
## Step: AIC=-2595.01
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 +
## vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE +
## DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR +
## NYG + NYJ + PHI + PIT + SEA + TB + TEN + WAS + avg_rectd_plyr +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - hot_weather 1 0.02 24935 -2597.0
## - HOU 1 0.02 24935 -2597.0
## - DEN 1 0.02 24935 -2597.0
## - SEA 1 0.06 24935 -2596.9
## - avg_rectd_plyr 1 0.07 24935 -2596.9
## - JAC 1 0.08 24935 -2596.9
## - bad_weather_1 1 0.09 24935 -2596.9
## - PHI 1 0.13 24935 -2596.9
## - NYG 1 0.14 24935 -2596.9
## - GB 1 0.15 24935 -2596.8
## - DET 1 0.15 24935 -2596.8
## - TB 1 0.16 24935 -2596.8
## - CLE 1 0.16 24935 -2596.8
## - forty1 1 0.19 24935 -2596.8
## - MINN 1 0.20 24935 -2596.8
## - ATL 1 0.24 24935 -2596.7
## - avg_rbry_plyr 1 0.24 24935 -2596.7
## - home_team_1 1 0.26 24935 -2596.7
## - WAS 1 0.28 24935 -2596.7
## - vertical1 1 0.33 24935 -2596.7
## - avg_rbry_pos 1 0.33 24935 -2596.7
## - DAL 1 0.36 24935 -2596.6
## - BUF 1 0.36 24935 -2596.6
## - height 1 0.43 24936 -2596.5
## - CAR 1 0.51 24936 -2596.4
## - PIT 1 0.52 24936 -2596.4
## - ARI 1 0.61 24936 -2596.3
## - BAL 1 0.78 24936 -2596.2
## - avg_qbtdp_plyr 1 0.88 24936 -2596.0
## - TEN 1 1.32 24936 -2595.6
## - CIN 1 1.54 24937 -2595.3
## - grass_1 1 1.58 24937 -2595.3
## <none> 24935 -2595.0
## - NE 1 2.08 24937 -2594.7
## - NOR 1 2.25 24937 -2594.5
## - IND 1 2.36 24937 -2594.4
## - cold_weather 1 3.27 24938 -2593.4
## - NYJ 1 3.27 24938 -2593.4
## - CHI 1 3.67 24939 -2593.0
## - avg_fuml_plyr 1 1212.24 26147 -1292.3
##
## Step: AIC=-2596.99
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYG + NYJ +
## PHI + PIT + SEA + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - HOU 1 0.02 24935 -2599.0
## - DEN 1 0.02 24935 -2599.0
## - SEA 1 0.06 24935 -2598.9
## - avg_rectd_plyr 1 0.07 24935 -2598.9
## - JAC 1 0.08 24935 -2598.9
## - bad_weather_1 1 0.09 24935 -2598.9
## - PHI 1 0.13 24935 -2598.8
## - NYG 1 0.14 24935 -2598.8
## - GB 1 0.15 24935 -2598.8
## - TB 1 0.15 24935 -2598.8
## - DET 1 0.16 24935 -2598.8
## - CLE 1 0.16 24935 -2598.8
## - forty1 1 0.19 24935 -2598.8
## - MINN 1 0.20 24935 -2598.8
## - avg_rbry_plyr 1 0.24 24935 -2598.7
## - ATL 1 0.24 24935 -2598.7
## - home_team_1 1 0.26 24935 -2598.7
## - WAS 1 0.29 24935 -2598.7
## - vertical1 1 0.33 24935 -2598.6
## - avg_rbry_pos 1 0.33 24935 -2598.6
## - BUF 1 0.36 24935 -2598.6
## - DAL 1 0.36 24935 -2598.6
## - height 1 0.43 24936 -2598.5
## - CAR 1 0.51 24936 -2598.4
## - PIT 1 0.52 24936 -2598.4
## - ARI 1 0.61 24936 -2598.3
## - BAL 1 0.78 24936 -2598.1
## - avg_qbtdp_plyr 1 0.88 24936 -2598.0
## - TEN 1 1.33 24936 -2597.5
## - CIN 1 1.54 24937 -2597.3
## - grass_1 1 1.57 24937 -2597.3
## <none> 24935 -2597.0
## - NE 1 2.08 24937 -2596.7
## - NOR 1 2.25 24937 -2596.5
## - IND 1 2.36 24937 -2596.4
## - cold_weather 1 3.25 24938 -2595.4
## - NYJ 1 3.26 24938 -2595.4
## - CHI 1 3.68 24939 -2594.9
## - avg_fuml_plyr 1 1212.29 26147 -1294.2
##
## Step: AIC=-2598.97
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN +
## DET + GB + IND + JAC + MINN + NE + NOR + NYG + NYJ + PHI +
## PIT + SEA + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 +
## bad_weather_1
##
## Df Sum of Sq RSS AIC
## - DEN 1 0.02 24935 -2600.9
## - JAC 1 0.07 24935 -2600.9
## - avg_rectd_plyr 1 0.07 24935 -2600.9
## - SEA 1 0.08 24935 -2600.9
## - bad_weather_1 1 0.08 24935 -2600.9
## - GB 1 0.14 24935 -2600.8
## - DET 1 0.14 24935 -2600.8
## - PHI 1 0.14 24935 -2600.8
## - TB 1 0.14 24935 -2600.8
## - CLE 1 0.15 24935 -2600.8
## - NYG 1 0.16 24935 -2600.8
## - MINN 1 0.18 24935 -2600.8
## - forty1 1 0.20 24935 -2600.8
## - ATL 1 0.23 24935 -2600.7
## - avg_rbry_plyr 1 0.25 24935 -2600.7
## - home_team_1 1 0.25 24935 -2600.7
## - WAS 1 0.27 24935 -2600.7
## - avg_rbry_pos 1 0.33 24935 -2600.6
## - vertical1 1 0.34 24935 -2600.6
## - BUF 1 0.34 24935 -2600.6
## - DAL 1 0.34 24935 -2600.6
## - height 1 0.43 24936 -2600.5
## - CAR 1 0.49 24936 -2600.4
## - PIT 1 0.50 24936 -2600.4
## - ARI 1 0.60 24936 -2600.3
## - BAL 1 0.77 24936 -2600.1
## - avg_qbtdp_plyr 1 0.88 24936 -2600.0
## - TEN 1 1.31 24936 -2599.5
## - CIN 1 1.52 24937 -2599.3
## - grass_1 1 1.55 24937 -2599.3
## <none> 24935 -2599.0
## - NE 1 2.07 24937 -2598.7
## - NOR 1 2.24 24937 -2598.5
## - IND 1 2.36 24937 -2598.4
## - NYJ 1 3.26 24938 -2597.4
## - cold_weather 1 3.27 24938 -2597.4
## - CHI 1 3.68 24939 -2596.9
## - avg_fuml_plyr 1 1213.13 26148 -1295.3
##
## Step: AIC=-2600.95
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET +
## GB + IND + JAC + MINN + NE + NOR + NYG + NYJ + PHI + PIT +
## SEA + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - JAC 1 0.06 24935 -2602.9
## - avg_rectd_plyr 1 0.08 24935 -2602.9
## - bad_weather_1 1 0.09 24935 -2602.9
## - SEA 1 0.09 24935 -2602.9
## - GB 1 0.13 24935 -2602.8
## - TB 1 0.13 24935 -2602.8
## - DET 1 0.13 24935 -2602.8
## - CLE 1 0.14 24935 -2602.8
## - PHI 1 0.16 24935 -2602.8
## - MINN 1 0.17 24935 -2602.8
## - NYG 1 0.17 24935 -2602.8
## - forty1 1 0.20 24935 -2602.7
## - ATL 1 0.22 24935 -2602.7
## - avg_rbry_plyr 1 0.25 24935 -2602.7
## - home_team_1 1 0.26 24935 -2602.7
## - WAS 1 0.26 24935 -2602.7
## - BUF 1 0.33 24935 -2602.6
## - DAL 1 0.33 24935 -2602.6
## - avg_rbry_pos 1 0.33 24935 -2602.6
## - vertical1 1 0.35 24935 -2602.6
## - height 1 0.44 24936 -2602.5
## - CAR 1 0.48 24936 -2602.4
## - PIT 1 0.48 24936 -2602.4
## - ARI 1 0.58 24936 -2602.3
## - BAL 1 0.75 24936 -2602.1
## - avg_qbtdp_plyr 1 0.88 24936 -2602.0
## - TEN 1 1.29 24936 -2601.5
## - CIN 1 1.51 24937 -2601.3
## - grass_1 1 1.57 24937 -2601.2
## <none> 24935 -2600.9
## - NE 1 2.05 24937 -2600.7
## - NOR 1 2.23 24937 -2600.5
## - IND 1 2.34 24937 -2600.4
## - cold_weather 1 3.25 24938 -2599.4
## - NYJ 1 3.25 24938 -2599.4
## - CHI 1 3.67 24939 -2598.9
## - avg_fuml_plyr 1 1213.27 26148 -1297.2
##
## Step: AIC=-2602.88
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET +
## GB + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA +
## TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - avg_rectd_plyr 1 0.08 24935 -2604.8
## - bad_weather_1 1 0.09 24935 -2604.8
## - SEA 1 0.11 24935 -2604.8
## - GB 1 0.11 24935 -2604.8
## - TB 1 0.11 24935 -2604.8
## - DET 1 0.12 24935 -2604.8
## - CLE 1 0.12 24935 -2604.8
## - MINN 1 0.15 24935 -2604.7
## - PHI 1 0.18 24935 -2604.7
## - ATL 1 0.20 24935 -2604.7
## - NYG 1 0.20 24935 -2604.7
## - forty1 1 0.21 24935 -2604.7
## - WAS 1 0.23 24935 -2604.6
## - avg_rbry_plyr 1 0.25 24935 -2604.6
## - home_team_1 1 0.26 24935 -2604.6
## - BUF 1 0.30 24936 -2604.6
## - DAL 1 0.30 24936 -2604.6
## - avg_rbry_pos 1 0.34 24936 -2604.5
## - vertical1 1 0.37 24936 -2604.5
## - height 1 0.45 24936 -2604.4
## - CAR 1 0.45 24936 -2604.4
## - PIT 1 0.45 24936 -2604.4
## - ARI 1 0.55 24936 -2604.3
## - BAL 1 0.71 24936 -2604.1
## - avg_qbtdp_plyr 1 0.89 24936 -2603.9
## - TEN 1 1.25 24936 -2603.5
## - CIN 1 1.46 24937 -2603.3
## - grass_1 1 1.58 24937 -2603.1
## <none> 24935 -2602.9
## - NE 1 2.00 24937 -2602.7
## - NOR 1 2.17 24937 -2602.5
## - IND 1 2.29 24938 -2602.4
## - NYJ 1 3.19 24938 -2601.4
## - cold_weather 1 3.28 24938 -2601.3
## - CHI 1 3.61 24939 -2600.9
## - avg_fuml_plyr 1 1213.63 26149 -1298.7
##
## Step: AIC=-2604.8
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET +
## GB + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA +
## TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1 + bad_weather_1
##
## Df Sum of Sq RSS AIC
## - bad_weather_1 1 0.09 24935 -2606.7
## - SEA 1 0.10 24935 -2606.7
## - CLE 1 0.11 24935 -2606.7
## - TB 1 0.11 24935 -2606.7
## - DET 1 0.13 24935 -2606.7
## - GB 1 0.13 24935 -2606.7
## - MINN 1 0.14 24935 -2606.6
## - PHI 1 0.18 24935 -2606.6
## - forty1 1 0.19 24935 -2606.6
## - NYG 1 0.19 24935 -2606.6
## - ATL 1 0.21 24936 -2606.6
## - WAS 1 0.23 24936 -2606.5
## - avg_rbry_plyr 1 0.25 24936 -2606.5
## - home_team_1 1 0.27 24936 -2606.5
## - BUF 1 0.30 24936 -2606.5
## - DAL 1 0.32 24936 -2606.4
## - vertical1 1 0.39 24936 -2606.4
## - height 1 0.40 24936 -2606.4
## - CAR 1 0.44 24936 -2606.3
## - PIT 1 0.46 24936 -2606.3
## - avg_rbry_pos 1 0.50 24936 -2606.2
## - ARI 1 0.54 24936 -2606.2
## - BAL 1 0.71 24936 -2606.0
## - avg_qbtdp_plyr 1 0.82 24936 -2605.9
## - TEN 1 1.23 24937 -2605.4
## - CIN 1 1.46 24937 -2605.2
## - grass_1 1 1.59 24937 -2605.0
## <none> 24935 -2604.8
## - NE 1 2.15 24937 -2604.4
## - NOR 1 2.28 24938 -2604.3
## - IND 1 2.31 24938 -2604.2
## - NYJ 1 3.18 24938 -2603.3
## - cold_weather 1 3.29 24939 -2603.2
## - CHI 1 3.60 24939 -2602.8
## - avg_fuml_plyr 1 1214.04 26149 -1300.2
##
## Step: AIC=-2606.7
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET +
## GB + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA +
## TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - CLE 1 0.10 24935 -2608.6
## - SEA 1 0.11 24935 -2608.6
## - TB 1 0.12 24935 -2608.6
## - DET 1 0.12 24936 -2608.6
## - GB 1 0.13 24936 -2608.6
## - MINN 1 0.14 24936 -2608.6
## - PHI 1 0.18 24936 -2608.5
## - forty1 1 0.18 24936 -2608.5
## - NYG 1 0.20 24936 -2608.5
## - ATL 1 0.21 24936 -2608.5
## - WAS 1 0.23 24936 -2608.4
## - avg_rbry_plyr 1 0.25 24936 -2608.4
## - home_team_1 1 0.26 24936 -2608.4
## - BUF 1 0.29 24936 -2608.4
## - DAL 1 0.32 24936 -2608.3
## - vertical1 1 0.39 24936 -2608.3
## - height 1 0.40 24936 -2608.3
## - CAR 1 0.44 24936 -2608.2
## - PIT 1 0.46 24936 -2608.2
## - avg_rbry_pos 1 0.50 24936 -2608.2
## - ARI 1 0.54 24936 -2608.1
## - BAL 1 0.71 24936 -2607.9
## - avg_qbtdp_plyr 1 0.81 24936 -2607.8
## - TEN 1 1.24 24937 -2607.3
## - CIN 1 1.45 24937 -2607.1
## - grass_1 1 1.57 24937 -2607.0
## <none> 24935 -2606.7
## - NE 1 2.12 24937 -2606.4
## - NOR 1 2.27 24938 -2606.2
## - IND 1 2.31 24938 -2606.2
## - NYJ 1 3.17 24939 -2605.2
## - cold_weather 1 3.49 24939 -2604.9
## - CHI 1 3.56 24939 -2604.8
## - avg_fuml_plyr 1 1213.96 26149 -1302.2
##
## Step: AIC=-2608.59
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + DET + GB +
## IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + TB +
## TEN + WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - TB 1 0.10 24936 -2610.5
## - GB 1 0.10 24936 -2610.5
## - DET 1 0.11 24936 -2610.5
## - MINN 1 0.12 24936 -2610.5
## - SEA 1 0.13 24936 -2610.4
## - forty1 1 0.19 24936 -2610.4
## - ATL 1 0.19 24936 -2610.4
## - WAS 1 0.20 24936 -2610.4
## - PHI 1 0.21 24936 -2610.4
## - NYG 1 0.23 24936 -2610.3
## - avg_rbry_plyr 1 0.25 24936 -2610.3
## - BUF 1 0.26 24936 -2610.3
## - home_team_1 1 0.27 24936 -2610.3
## - DAL 1 0.29 24936 -2610.3
## - vertical1 1 0.40 24936 -2610.2
## - CAR 1 0.40 24936 -2610.2
## - height 1 0.41 24936 -2610.1
## - PIT 1 0.41 24936 -2610.1
## - ARI 1 0.50 24936 -2610.0
## - avg_rbry_pos 1 0.51 24936 -2610.0
## - BAL 1 0.67 24936 -2609.8
## - avg_qbtdp_plyr 1 0.80 24936 -2609.7
## - TEN 1 1.18 24937 -2609.3
## - CIN 1 1.39 24937 -2609.1
## - grass_1 1 1.59 24937 -2608.8
## <none> 24935 -2608.6
## - NE 1 2.05 24938 -2608.3
## - NOR 1 2.20 24938 -2608.2
## - IND 1 2.24 24938 -2608.1
## - NYJ 1 3.09 24939 -2607.2
## - cold_weather 1 3.41 24939 -2606.8
## - CHI 1 3.48 24939 -2606.8
## - avg_fuml_plyr 1 1214.82 26150 -1303.2
##
## Step: AIC=-2610.48
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + DET + GB +
## IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + TEN +
## WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - GB 1 0.09 24936 -2612.4
## - DET 1 0.09 24936 -2612.4
## - MINN 1 0.10 24936 -2612.4
## - SEA 1 0.15 24936 -2612.3
## - ATL 1 0.17 24936 -2612.3
## - WAS 1 0.18 24936 -2612.3
## - forty1 1 0.19 24936 -2612.3
## - PHI 1 0.23 24936 -2612.2
## - BUF 1 0.24 24936 -2612.2
## - avg_rbry_plyr 1 0.25 24936 -2612.2
## - NYG 1 0.26 24936 -2612.2
## - DAL 1 0.26 24936 -2612.2
## - home_team_1 1 0.28 24936 -2612.2
## - CAR 1 0.37 24936 -2612.1
## - PIT 1 0.38 24936 -2612.1
## - vertical1 1 0.39 24936 -2612.1
## - height 1 0.40 24936 -2612.0
## - ARI 1 0.47 24936 -2612.0
## - avg_rbry_pos 1 0.51 24936 -2611.9
## - BAL 1 0.63 24936 -2611.8
## - avg_qbtdp_plyr 1 0.79 24936 -2611.6
## - TEN 1 1.13 24937 -2611.2
## - CIN 1 1.33 24937 -2611.0
## - grass_1 1 1.60 24937 -2610.7
## <none> 24936 -2610.5
## - NE 1 1.99 24938 -2610.3
## - NOR 1 2.14 24938 -2610.1
## - IND 1 2.18 24938 -2610.1
## - NYJ 1 3.01 24939 -2609.2
## - CHI 1 3.40 24939 -2608.7
## - cold_weather 1 3.47 24939 -2608.7
## - avg_fuml_plyr 1 1214.75 26150 -1305.2
##
## Step: AIC=-2612.39
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + DET + IND +
## MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + TEN + WAS +
## avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - DET 1 0.08 24936 -2614.3
## - MINN 1 0.09 24936 -2614.3
## - ATL 1 0.15 24936 -2614.2
## - WAS 1 0.16 24936 -2614.2
## - SEA 1 0.18 24936 -2614.2
## - forty1 1 0.19 24936 -2614.2
## - BUF 1 0.22 24936 -2614.2
## - DAL 1 0.24 24936 -2614.1
## - avg_rbry_plyr 1 0.25 24936 -2614.1
## - PHI 1 0.26 24936 -2614.1
## - NYG 1 0.29 24936 -2614.1
## - home_team_1 1 0.29 24936 -2614.1
## - CAR 1 0.34 24936 -2614.0
## - PIT 1 0.35 24936 -2614.0
## - vertical1 1 0.38 24936 -2614.0
## - height 1 0.41 24936 -2613.9
## - ARI 1 0.44 24936 -2613.9
## - avg_rbry_pos 1 0.52 24936 -2613.8
## - BAL 1 0.59 24936 -2613.7
## - avg_qbtdp_plyr 1 0.82 24936 -2613.5
## - TEN 1 1.09 24937 -2613.2
## - CIN 1 1.28 24937 -2613.0
## - grass_1 1 1.60 24937 -2612.6
## <none> 24936 -2612.4
## - NE 1 1.92 24938 -2612.3
## - NOR 1 2.08 24938 -2612.1
## - IND 1 2.12 24938 -2612.1
## - NYJ 1 2.95 24939 -2611.1
## - CHI 1 3.33 24939 -2610.7
## - cold_weather 1 3.40 24939 -2610.6
## - avg_fuml_plyr 1 1218.18 26154 -1303.5
##
## Step: AIC=-2614.3
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + IND + MINN +
## NE + NOR + NYG + NYJ + PHI + PIT + SEA + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - MINN 1 0.08 24936 -2616.2
## - ATL 1 0.13 24936 -2616.2
## - WAS 1 0.14 24936 -2616.2
## - forty1 1 0.19 24936 -2616.1
## - BUF 1 0.19 24936 -2616.1
## - SEA 1 0.20 24936 -2616.1
## - DAL 1 0.22 24936 -2616.1
## - avg_rbry_plyr 1 0.25 24936 -2616.0
## - home_team_1 1 0.27 24936 -2616.0
## - PHI 1 0.28 24936 -2616.0
## - NYG 1 0.32 24936 -2615.9
## - CAR 1 0.32 24936 -2615.9
## - PIT 1 0.33 24936 -2615.9
## - vertical1 1 0.39 24936 -2615.9
## - height 1 0.41 24936 -2615.8
## - ARI 1 0.41 24936 -2615.8
## - avg_rbry_pos 1 0.51 24936 -2615.7
## - BAL 1 0.56 24936 -2615.7
## - avg_qbtdp_plyr 1 0.82 24937 -2615.4
## - TEN 1 1.05 24937 -2615.1
## - CIN 1 1.24 24937 -2614.9
## - grass_1 1 1.54 24937 -2614.6
## <none> 24936 -2614.3
## - NE 1 1.87 24938 -2614.2
## - NOR 1 2.02 24938 -2614.1
## - IND 1 2.06 24938 -2614.0
## - NYJ 1 2.89 24939 -2613.1
## - CHI 1 3.28 24939 -2612.7
## - cold_weather 1 3.44 24939 -2612.5
## - avg_fuml_plyr 1 1218.29 26154 -1305.3
##
## Step: AIC=-2616.22
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + IND + NE +
## NOR + NYG + NYJ + PHI + PIT + SEA + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - ATL 1 0.12 24936 -2618.1
## - WAS 1 0.13 24936 -2618.1
## - BUF 1 0.18 24936 -2618.0
## - forty1 1 0.19 24936 -2618.0
## - DAL 1 0.20 24936 -2618.0
## - SEA 1 0.23 24936 -2618.0
## - avg_rbry_plyr 1 0.26 24936 -2617.9
## - home_team_1 1 0.28 24936 -2617.9
## - CAR 1 0.30 24936 -2617.9
## - PHI 1 0.30 24936 -2617.9
## - PIT 1 0.31 24936 -2617.9
## - NYG 1 0.35 24936 -2617.8
## - ARI 1 0.38 24936 -2617.8
## - height 1 0.40 24936 -2617.8
## - vertical1 1 0.40 24936 -2617.8
## - avg_rbry_pos 1 0.51 24936 -2617.7
## - BAL 1 0.53 24936 -2617.6
## - avg_qbtdp_plyr 1 0.82 24937 -2617.3
## - TEN 1 1.02 24937 -2617.1
## - CIN 1 1.19 24937 -2616.9
## - grass_1 1 1.48 24937 -2616.6
## <none> 24936 -2616.2
## - NE 1 1.82 24938 -2616.2
## - NOR 1 1.96 24938 -2616.1
## - IND 1 2.01 24938 -2616.0
## - NYJ 1 2.83 24939 -2615.1
## - CHI 1 3.23 24939 -2614.7
## - cold_weather 1 3.42 24939 -2614.4
## - avg_fuml_plyr 1 1218.34 26154 -1307.1
##
## Step: AIC=-2618.09
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + BAL + BUF + CAR + CHI + CIN + DAL + IND + NE + NOR +
## NYG + NYJ + PHI + PIT + SEA + TEN + WAS + avg_rbry_plyr +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - WAS 1 0.12 24936 -2620.0
## - BUF 1 0.16 24936 -2619.9
## - DAL 1 0.17 24936 -2619.9
## - forty1 1 0.19 24936 -2619.9
## - home_team_1 1 0.24 24936 -2619.8
## - SEA 1 0.25 24936 -2619.8
## - avg_rbry_plyr 1 0.26 24936 -2619.8
## - CAR 1 0.28 24936 -2619.8
## - PIT 1 0.29 24936 -2619.8
## - PHI 1 0.32 24936 -2619.7
## - ARI 1 0.35 24936 -2619.7
## - NYG 1 0.38 24936 -2619.7
## - vertical1 1 0.38 24936 -2619.7
## - height 1 0.42 24936 -2619.6
## - BAL 1 0.49 24936 -2619.5
## - avg_rbry_pos 1 0.52 24936 -2619.5
## - avg_qbtdp_plyr 1 0.84 24937 -2619.2
## - TEN 1 0.99 24937 -2619.0
## - CIN 1 1.15 24937 -2618.8
## - grass_1 1 1.41 24937 -2618.5
## - NE 1 1.75 24938 -2618.2
## <none> 24936 -2618.1
## - NOR 1 1.89 24938 -2618.0
## - IND 1 1.94 24938 -2617.9
## - NYJ 1 2.76 24939 -2617.1
## - CHI 1 3.18 24939 -2616.6
## - cold_weather 1 3.49 24939 -2616.2
## - avg_fuml_plyr 1 1222.16 26158 -1305.0
##
## Step: AIC=-2619.96
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + BAL + BUF + CAR + CHI + CIN + DAL + IND + NE + NOR +
## NYG + NYJ + PHI + PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - BUF 1 0.14 24936 -2621.8
## - DAL 1 0.16 24936 -2621.8
## - forty1 1 0.18 24936 -2621.8
## - avg_rbry_plyr 1 0.25 24936 -2621.7
## - home_team_1 1 0.25 24936 -2621.7
## - CAR 1 0.26 24936 -2621.7
## - PIT 1 0.27 24936 -2621.7
## - SEA 1 0.28 24936 -2621.7
## - ARI 1 0.33 24936 -2621.6
## - PHI 1 0.35 24936 -2621.6
## - vertical1 1 0.38 24936 -2621.5
## - NYG 1 0.40 24936 -2621.5
## - height 1 0.44 24936 -2621.5
## - BAL 1 0.47 24937 -2621.4
## - avg_rbry_pos 1 0.53 24937 -2621.4
## - avg_qbtdp_plyr 1 0.85 24937 -2621.0
## - TEN 1 0.94 24937 -2620.9
## - CIN 1 1.11 24937 -2620.7
## - grass_1 1 1.44 24937 -2620.4
## - NE 1 1.71 24938 -2620.1
## <none> 24936 -2620.0
## - NOR 1 1.84 24938 -2619.9
## - IND 1 1.89 24938 -2619.9
## - NYJ 1 2.70 24939 -2619.0
## - CHI 1 3.11 24939 -2618.5
## - cold_weather 1 3.47 24940 -2618.1
## - avg_fuml_plyr 1 1222.52 26159 -1306.5
##
## Step: AIC=-2621.81
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + BAL + CAR + CHI + CIN + DAL + IND + NE + NOR + NYG +
## NYJ + PHI + PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - DAL 1 0.14 24936 -2623.7
## - forty1 1 0.16 24936 -2623.6
## - CAR 1 0.24 24936 -2623.5
## - PIT 1 0.25 24936 -2623.5
## - avg_rbry_plyr 1 0.25 24936 -2623.5
## - home_team_1 1 0.27 24936 -2623.5
## - ARI 1 0.30 24936 -2623.5
## - SEA 1 0.31 24937 -2623.5
## - vertical1 1 0.36 24937 -2623.4
## - PHI 1 0.38 24937 -2623.4
## - height 1 0.42 24937 -2623.3
## - BAL 1 0.43 24937 -2623.3
## - NYG 1 0.45 24937 -2623.3
## - avg_rbry_pos 1 0.52 24937 -2623.2
## - avg_qbtdp_plyr 1 0.84 24937 -2622.9
## - TEN 1 0.91 24937 -2622.8
## - CIN 1 1.05 24937 -2622.7
## - grass_1 1 1.35 24938 -2622.3
## - NE 1 1.64 24938 -2622.0
## - NOR 1 1.78 24938 -2621.8
## <none> 24936 -2621.8
## - IND 1 1.83 24938 -2621.8
## - NYJ 1 2.62 24939 -2620.9
## - CHI 1 3.04 24939 -2620.4
## - cold_weather 1 3.40 24940 -2620.1
## - avg_fuml_plyr 1 1222.44 26159 -1308.5
##
## Step: AIC=-2623.65
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 +
## ARI + BAL + CAR + CHI + CIN + IND + NE + NOR + NYG + NYJ +
## PHI + PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - forty1 1 0.16 24936 -2625.5
## - CAR 1 0.22 24937 -2625.4
## - PIT 1 0.23 24937 -2625.4
## - home_team_1 1 0.24 24937 -2625.4
## - avg_rbry_plyr 1 0.26 24937 -2625.4
## - ARI 1 0.27 24937 -2625.4
## - SEA 1 0.34 24937 -2625.3
## - vertical1 1 0.36 24937 -2625.3
## - PHI 1 0.40 24937 -2625.2
## - BAL 1 0.41 24937 -2625.2
## - height 1 0.42 24937 -2625.2
## - NYG 1 0.48 24937 -2625.1
## - avg_rbry_pos 1 0.53 24937 -2625.1
## - avg_qbtdp_plyr 1 0.85 24937 -2624.7
## - TEN 1 0.88 24937 -2624.7
## - CIN 1 1.01 24937 -2624.5
## - grass_1 1 1.28 24938 -2624.2
## - NE 1 1.59 24938 -2623.9
## - NOR 1 1.72 24938 -2623.8
## - IND 1 1.76 24938 -2623.7
## <none> 24936 -2623.7
## - NYJ 1 2.56 24939 -2622.8
## - CHI 1 2.99 24939 -2622.3
## - cold_weather 1 3.43 24940 -2621.9
## - avg_fuml_plyr 1 1222.72 26159 -1310.0
##
## Step: AIC=-2625.48
## fuml ~ height + cold_weather + home_team_1 + vertical1 + ARI +
## BAL + CAR + CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI +
## PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - avg_rbry_plyr 1 0.20 24937 -2627.3
## - vertical1 1 0.21 24937 -2627.2
## - CAR 1 0.22 24937 -2627.2
## - PIT 1 0.23 24937 -2627.2
## - home_team_1 1 0.23 24937 -2627.2
## - ARI 1 0.25 24937 -2627.2
## - height 1 0.28 24937 -2627.2
## - SEA 1 0.35 24937 -2627.1
## - BAL 1 0.41 24937 -2627.0
## - PHI 1 0.41 24937 -2627.0
## - avg_rbry_pos 1 0.44 24937 -2627.0
## - NYG 1 0.47 24937 -2627.0
## - TEN 1 0.88 24937 -2626.5
## - CIN 1 1.01 24937 -2626.4
## - avg_qbtdp_plyr 1 1.10 24938 -2626.3
## - grass_1 1 1.27 24938 -2626.1
## - NOR 1 1.69 24938 -2625.6
## - NE 1 1.70 24938 -2625.6
## - IND 1 1.77 24938 -2625.5
## <none> 24936 -2625.5
## - NYJ 1 2.60 24939 -2624.6
## - CHI 1 2.95 24939 -2624.2
## - cold_weather 1 3.42 24940 -2623.7
## - avg_fuml_plyr 1 1225.11 26162 -1309.3
##
## Step: AIC=-2627.26
## fuml ~ height + cold_weather + home_team_1 + vertical1 + ARI +
## BAL + CAR + CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI +
## PIT + SEA + TEN + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - vertical1 1 0.23 24937 -2629.0
## - CAR 1 0.23 24937 -2629.0
## - home_team_1 1 0.23 24937 -2629.0
## - PIT 1 0.23 24937 -2629.0
## - avg_rbry_pos 1 0.24 24937 -2629.0
## - ARI 1 0.24 24937 -2629.0
## - height 1 0.28 24937 -2628.9
## - SEA 1 0.33 24937 -2628.9
## - PHI 1 0.40 24937 -2628.8
## - BAL 1 0.40 24937 -2628.8
## - NYG 1 0.48 24937 -2628.7
## - TEN 1 0.88 24938 -2628.3
## - avg_qbtdp_plyr 1 0.96 24938 -2628.2
## - CIN 1 1.03 24938 -2628.1
## - grass_1 1 1.27 24938 -2627.9
## - NOR 1 1.67 24938 -2627.4
## - NE 1 1.73 24938 -2627.3
## - IND 1 1.77 24938 -2627.3
## <none> 24937 -2627.3
## - NYJ 1 2.62 24939 -2626.4
## - CHI 1 2.97 24940 -2626.0
## - cold_weather 1 3.42 24940 -2625.5
## - avg_fuml_plyr 1 1371.11 26308 -1158.2
##
## Step: AIC=-2629.01
## fuml ~ height + cold_weather + home_team_1 + ARI + BAL + CAR +
## CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI + PIT + SEA +
## TEN + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - PIT 1 0.23 24937 -2630.8
## - home_team_1 1 0.24 24937 -2630.7
## - ARI 1 0.24 24937 -2630.7
## - CAR 1 0.24 24937 -2630.7
## - SEA 1 0.31 24937 -2630.7
## - avg_rbry_pos 1 0.33 24937 -2630.7
## - height 1 0.38 24937 -2630.6
## - BAL 1 0.40 24937 -2630.6
## - PHI 1 0.41 24937 -2630.6
## - NYG 1 0.49 24937 -2630.5
## - avg_qbtdp_plyr 1 0.79 24938 -2630.1
## - TEN 1 0.89 24938 -2630.0
## - CIN 1 1.01 24938 -2629.9
## - grass_1 1 1.28 24938 -2629.6
## - NE 1 1.66 24939 -2629.2
## - NOR 1 1.71 24939 -2629.1
## <none> 24937 -2629.0
## - IND 1 1.82 24939 -2629.0
## - NYJ 1 2.71 24940 -2628.0
## - CHI 1 2.94 24940 -2627.8
## - cold_weather 1 3.41 24940 -2627.2
## - avg_fuml_plyr 1 1370.93 26308 -1160.1
##
## Step: AIC=-2630.75
## fuml ~ height + cold_weather + home_team_1 + ARI + BAL + CAR +
## CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI + SEA + TEN +
## avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - CAR 1 0.22 24937 -2632.5
## - ARI 1 0.22 24937 -2632.5
## - home_team_1 1 0.25 24937 -2632.5
## - avg_rbry_pos 1 0.33 24937 -2632.4
## - SEA 1 0.34 24937 -2632.4
## - BAL 1 0.37 24938 -2632.3
## - height 1 0.38 24938 -2632.3
## - PHI 1 0.45 24938 -2632.2
## - NYG 1 0.53 24938 -2632.2
## - avg_qbtdp_plyr 1 0.79 24938 -2631.9
## - TEN 1 0.84 24938 -2631.8
## - CIN 1 0.97 24938 -2631.7
## - grass_1 1 1.35 24938 -2631.3
## - NE 1 1.59 24939 -2631.0
## - NOR 1 1.66 24939 -2630.9
## - IND 1 1.77 24939 -2630.8
## <none> 24937 -2630.8
## - NYJ 1 2.63 24940 -2629.8
## - CHI 1 2.85 24940 -2629.6
## - cold_weather 1 3.27 24940 -2629.1
## - avg_fuml_plyr 1 1370.76 26308 -1162.0
##
## Step: AIC=-2632.51
## fuml ~ height + cold_weather + home_team_1 + ARI + BAL + CHI +
## CIN + IND + NE + NOR + NYG + NYJ + PHI + SEA + TEN + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - ARI 1 0.20 24938 -2634.3
## - home_team_1 1 0.27 24938 -2634.2
## - avg_rbry_pos 1 0.33 24938 -2634.1
## - BAL 1 0.34 24938 -2634.1
## - SEA 1 0.37 24938 -2634.1
## - height 1 0.38 24938 -2634.1
## - PHI 1 0.49 24938 -2634.0
## - NYG 1 0.56 24938 -2633.9
## - avg_qbtdp_plyr 1 0.78 24938 -2633.7
## - TEN 1 0.80 24938 -2633.6
## - CIN 1 0.93 24938 -2633.5
## - grass_1 1 1.40 24939 -2633.0
## - NE 1 1.54 24939 -2632.8
## - NOR 1 1.61 24939 -2632.7
## - IND 1 1.72 24939 -2632.6
## <none> 24937 -2632.5
## - NYJ 1 2.57 24940 -2631.7
## - CHI 1 2.78 24940 -2631.4
## - cold_weather 1 3.29 24941 -2630.9
## - avg_fuml_plyr 1 1370.61 26308 -1164.0
##
## Step: AIC=-2634.28
## fuml ~ height + cold_weather + home_team_1 + BAL + CHI + CIN +
## IND + NE + NOR + NYG + NYJ + PHI + SEA + TEN + avg_rbry_pos +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - home_team_1 1 0.22 24938 -2636.0
## - BAL 1 0.32 24938 -2635.9
## - avg_rbry_pos 1 0.33 24938 -2635.9
## - height 1 0.37 24938 -2635.9
## - SEA 1 0.40 24938 -2635.8
## - PHI 1 0.51 24938 -2635.7
## - NYG 1 0.60 24938 -2635.6
## - avg_qbtdp_plyr 1 0.77 24938 -2635.4
## - TEN 1 0.77 24938 -2635.4
## - CIN 1 0.88 24938 -2635.3
## - grass_1 1 1.32 24939 -2634.8
## - NE 1 1.49 24939 -2634.6
## - NOR 1 1.54 24939 -2634.6
## - IND 1 1.65 24939 -2634.5
## <none> 24938 -2634.3
## - NYJ 1 2.50 24940 -2633.5
## - CHI 1 2.72 24940 -2633.3
## - cold_weather 1 3.30 24941 -2632.7
## - avg_fuml_plyr 1 1370.41 26308 -1166.0
##
## Step: AIC=-2636.04
## fuml ~ height + cold_weather + BAL + CHI + CIN + IND + NE + NOR +
## NYG + NYJ + PHI + SEA + TEN + avg_rbry_pos + avg_fuml_plyr +
## avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - avg_rbry_pos 1 0.34 24938 -2637.7
## - BAL 1 0.35 24938 -2637.7
## - SEA 1 0.36 24938 -2637.6
## - height 1 0.37 24938 -2637.6
## - PHI 1 0.49 24938 -2637.5
## - NYG 1 0.56 24938 -2637.4
## - avg_qbtdp_plyr 1 0.76 24939 -2637.2
## - TEN 1 0.80 24939 -2637.2
## - CIN 1 0.94 24939 -2637.0
## - NOR 1 1.51 24939 -2636.4
## - IND 1 1.58 24939 -2636.3
## - NE 1 1.59 24939 -2636.3
## - grass_1 1 1.67 24939 -2636.2
## <none> 24938 -2636.0
## - NYJ 1 2.60 24940 -2635.2
## - CHI 1 2.76 24941 -2635.0
## - cold_weather 1 3.17 24941 -2634.6
## - avg_fuml_plyr 1 1370.19 26308 -1168.0
##
## Step: AIC=-2637.67
## fuml ~ height + cold_weather + BAL + CHI + CIN + IND + NE + NOR +
## NYG + NYJ + PHI + SEA + TEN + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - height 1 0.15 24938 -2639.5
## - BAL 1 0.34 24938 -2639.3
## - SEA 1 0.35 24938 -2639.3
## - PHI 1 0.47 24939 -2639.2
## - NYG 1 0.57 24939 -2639.0
## - avg_qbtdp_plyr 1 0.81 24939 -2638.8
## - TEN 1 0.82 24939 -2638.8
## - CIN 1 0.95 24939 -2638.6
## - NOR 1 1.48 24940 -2638.0
## - NE 1 1.58 24940 -2637.9
## - IND 1 1.63 24940 -2637.9
## - grass_1 1 1.68 24940 -2637.8
## <none> 24938 -2637.7
## - NYJ 1 2.63 24941 -2636.8
## - CHI 1 2.78 24941 -2636.6
## - cold_weather 1 3.17 24941 -2636.2
## - avg_fuml_plyr 1 1465.76 26404 -1070.0
##
## Step: AIC=-2639.5
## fuml ~ cold_weather + BAL + CHI + CIN + IND + NE + NOR + NYG +
## NYJ + PHI + SEA + TEN + avg_fuml_plyr + avg_qbtdp_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - BAL 1 0.33 24939 -2641.1
## - SEA 1 0.33 24939 -2641.1
## - PHI 1 0.46 24939 -2641.0
## - NYG 1 0.58 24939 -2640.9
## - avg_qbtdp_plyr 1 0.67 24939 -2640.8
## - TEN 1 0.82 24939 -2640.6
## - CIN 1 0.95 24939 -2640.4
## - NOR 1 1.52 24940 -2639.8
## - NE 1 1.64 24940 -2639.7
## - IND 1 1.66 24940 -2639.7
## - grass_1 1 1.69 24940 -2639.6
## <none> 24938 -2639.5
## - NYJ 1 2.63 24941 -2638.6
## - CHI 1 2.74 24941 -2638.5
## - cold_weather 1 3.16 24941 -2638.0
## - avg_fuml_plyr 1 1506.14 26444 -1029.8
##
## Step: AIC=-2641.14
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYG + NYJ +
## PHI + SEA + TEN + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - SEA 1 0.38 24939 -2642.7
## - PHI 1 0.50 24939 -2642.6
## - NYG 1 0.63 24939 -2642.4
## - avg_qbtdp_plyr 1 0.70 24939 -2642.4
## - TEN 1 0.78 24939 -2642.3
## - CIN 1 0.89 24940 -2642.2
## - NOR 1 1.44 24940 -2641.6
## - NE 1 1.55 24940 -2641.4
## - IND 1 1.58 24940 -2641.4
## - grass_1 1 1.60 24940 -2641.4
## <none> 24939 -2641.1
## - NYJ 1 2.54 24941 -2640.3
## - CHI 1 2.66 24941 -2640.2
## - cold_weather 1 3.04 24942 -2639.8
## - avg_fuml_plyr 1 1508.77 26447 -1028.7
##
## Step: AIC=-2642.72
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYG + NYJ +
## PHI + TEN + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - PHI 1 0.47 24939 -2644.2
## - NYG 1 0.58 24940 -2644.1
## - avg_qbtdp_plyr 1 0.68 24940 -2644.0
## - TEN 1 0.82 24940 -2643.8
## - CIN 1 0.97 24940 -2643.7
## - NOR 1 1.54 24941 -2643.0
## - NE 1 1.67 24941 -2642.9
## - IND 1 1.68 24941 -2642.9
## <none> 24939 -2642.7
## - grass_1 1 1.82 24941 -2642.7
## - NYJ 1 2.66 24942 -2641.8
## - CHI 1 2.74 24942 -2641.7
## - cold_weather 1 3.21 24942 -2641.2
## - avg_fuml_plyr 1 1508.81 26448 -1030.3
##
## Step: AIC=-2644.21
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYG + NYJ +
## TEN + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - NYG 1 0.54 24940 -2645.6
## - avg_qbtdp_plyr 1 0.71 24940 -2645.4
## - TEN 1 0.88 24940 -2645.2
## - CIN 1 1.02 24940 -2645.1
## - NOR 1 1.60 24941 -2644.4
## - NE 1 1.73 24941 -2644.3
## - grass_1 1 1.73 24941 -2644.3
## - IND 1 1.74 24941 -2644.3
## <none> 24939 -2644.2
## - NYJ 1 2.75 24942 -2643.2
## - CHI 1 2.85 24942 -2643.1
## - cold_weather 1 3.26 24943 -2642.6
## - avg_fuml_plyr 1 1515.63 26455 -1024.7
##
## Step: AIC=-2645.61
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYJ + TEN +
## avg_fuml_plyr + avg_qbtdp_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - avg_qbtdp_plyr 1 0.70 24941 -2646.8
## - TEN 1 0.92 24941 -2646.6
## - CIN 1 1.10 24941 -2646.4
## - NOR 1 1.70 24942 -2645.7
## <none> 24940 -2645.6
## - IND 1 1.85 24942 -2645.6
## - NE 1 1.85 24942 -2645.6
## - grass_1 1 1.96 24942 -2645.4
## - NYJ 1 2.89 24943 -2644.4
## - CHI 1 2.94 24943 -2644.4
## - cold_weather 1 3.42 24943 -2643.8
## - avg_fuml_plyr 1 1515.79 26456 -1026.0
##
## Step: AIC=-2646.83
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYJ + TEN +
## avg_fuml_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - TEN 1 0.89 24942 -2647.85
## - CIN 1 1.11 24942 -2647.61
## - NOR 1 1.81 24943 -2646.84
## <none> 24941 -2646.83
## - IND 1 1.88 24943 -2646.76
## - grass_1 1 1.95 24943 -2646.69
## - NE 1 2.02 24943 -2646.61
## - NYJ 1 2.81 24944 -2645.74
## - CHI 1 2.88 24944 -2645.66
## - cold_weather 1 3.41 24944 -2645.08
## - avg_fuml_plyr 1 2528.17 27469 4.81
##
## Step: AIC=-2647.85
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYJ + avg_fuml_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - CIN 1 1.06 24943 -2648.68
## - NOR 1 1.72 24943 -2647.95
## - IND 1 1.81 24943 -2647.86
## <none> 24942 -2647.85
## - NE 1 1.94 24944 -2647.71
## - grass_1 1 2.16 24944 -2647.46
## - NYJ 1 2.71 24944 -2646.86
## - CHI 1 2.75 24944 -2646.81
## - cold_weather 1 3.49 24945 -2646.00
## - avg_fuml_plyr 1 2527.57 27469 3.11
##
## Step: AIC=-2648.68
## fuml ~ cold_weather + CHI + IND + NE + NOR + NYJ + avg_fuml_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - NOR 1 1.61 24944 -2648.92
## - IND 1 1.69 24944 -2648.83
## - NE 1 1.80 24944 -2648.70
## <none> 24943 -2648.68
## - grass_1 1 1.89 24945 -2648.60
## - NYJ 1 2.56 24945 -2647.86
## - CHI 1 2.65 24945 -2647.76
## - cold_weather 1 3.30 24946 -2647.05
## - avg_fuml_plyr 1 2527.03 27470 1.63
##
## Step: AIC=-2648.92
## fuml ~ cold_weather + CHI + IND + NE + NYJ + avg_fuml_plyr +
## grass_1
##
## Df Sum of Sq RSS AIC
## - IND 1 1.54 24946 -2649.22
## - grass_1 1 1.58 24946 -2649.17
## - NE 1 1.65 24946 -2649.10
## <none> 24944 -2648.92
## - NYJ 1 2.38 24947 -2648.29
## - CHI 1 2.54 24947 -2648.12
## - cold_weather 1 3.51 24948 -2647.05
## - avg_fuml_plyr 1 2528.54 27473 2.74
##
## Step: AIC=-2649.22
## fuml ~ cold_weather + CHI + NE + NYJ + avg_fuml_plyr + grass_1
##
## Df Sum of Sq RSS AIC
## - grass_1 1 1.31 24947 -2649.78
## - NE 1 1.52 24947 -2649.55
## <none> 24946 -2649.22
## - NYJ 1 2.23 24948 -2648.77
## - CHI 1 2.44 24948 -2648.54
## - cold_weather 1 3.56 24949 -2647.30
## - avg_fuml_plyr 1 2527.83 27474 1.57
##
## Step: AIC=-2649.78
## fuml ~ cold_weather + CHI + NE + NYJ + avg_fuml_plyr
##
## Df Sum of Sq RSS AIC
## - NE 1 1.25 24948 -2650.40
## <none> 24947 -2649.78
## - NYJ 1 1.94 24949 -2649.64
## - CHI 1 2.69 24950 -2648.81
## - cold_weather 1 3.26 24950 -2648.18
## - avg_fuml_plyr 1 2526.94 27474 -0.01
##
## Step: AIC=-2650.4
## fuml ~ cold_weather + CHI + NYJ + avg_fuml_plyr
##
## Df Sum of Sq RSS AIC
## <none> 24948 -2650.40
## - NYJ 1 1.84 24950 -2650.38
## - CHI 1 2.57 24951 -2649.57
## - cold_weather 1 2.99 24951 -2649.10
## - avg_fuml_plyr 1 2532.79 27481 5.09Conclusions
Rushing and passing data seems to be something that linear regression has better predictions for that receiving. This makes sense. RB’s and QB’s are generally singular players on the field. Both are heavily invested in by teams and are given a lot of touches every game. Receiving is a little more spread out. There are generally at minimum, 3 players in a receiving capacity (excluding the RB), 2 WR and a TE. There can be up to 4 WR on the field, so trying to predict who gets the ball will be harder because it is more uncertain.
RB’s are negatively effected by age, the data supports this well known fact, I was glad to see that relationship.
Fumbles and INTs are also going to be hard to predict because they are generally random, but highly dependent upon the player carrying the ball and the defense they are playing against.
The data seems to have some skewness, so I may have to explore other options for predicting.
Going forward, I would like to explore more fields, I have completely ignored the opponents in this analysis, and would like to add them in for the future.
As mentioned above, baseball will be better for predicting because of the nature of the game: One batter vs one pitcher. I would like to build an analysis for baseball based on a similar method as I have used for this.
Appendix
Charts
WR targets by avg yards per player
ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
geom_point()+
geom_text(data = subset(nfl_data, avg_recy_plyr > 75), aes(label = pname), size = 2.5)
There are few anomalies in this graph, not surprising, the amount of targets correlates with the amount of yards a player gets. The top right corner is “ALL PRO” corner.
**Tight ends should not be compared to WR
ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
geom_point(data = subset(nfl_data, pos1 == "TE"))+
geom_text(data = subset(nfl_data, avg_recy_plyr > 50 & pos1 == "TE"), aes(label = pname), size = 2.5)
I separated out the TE from the WR. TE are not “homerun” hitters, but are frequent targets of QB’s. Rob Gronkowski is the biggest anomaly here, he is widely considered the best position player to ever play.
** RB’s separated out
ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
geom_point(data = subset(nfl_data, pos1 == "RB"))+
geom_text(data = subset(nfl_data, avg_recy_plyr > 30 & pos1 == "RB"), aes(label = pname), size = 2.5)
CJ prosise was a rookie who had a couple of explosive games. He is a RB who played WR in college. He switched to RB his senior year of college and became an elite RB. This trend will regress somewhat, however, he is a very legit dual threat.
**WR only
ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
geom_point(data = subset(nfl_data, pos1 == "WR"))+
geom_text(data = subset(nfl_data, avg_recy_plyr > 70 & pos1 == "WR"), aes(label = pname), size = 2.5)